 Get an effective help in learning problemsolving skills and grasping math concepts! EMSolution offers an infinite number of fully explained solutions. Each solution evolves step by step; each step of solution is provided with its objective, grounding definition and rule and with underlying formula or theorem. EMSolution encourages students to learn through indepth understanding of each solution step and repetition rather than through rote memorization. You can review solutions step by step, learn related math concepts, study solution methods, try to solve similar math problems on your own, and in parallel, learn math lexicon in a foreign language! For math teachers, EMSolution offers a number of easytouse test authoring options. You can select problems by topic, solution method and complexity level, prepare printable math tests and develop numerous test variants literally in a minute. A difficulty scale for each task will assist teachers in a class of mixed ability students. Free fully functional downloadable version of EMSolution is available. Free online demos allow trying most of the user options and viewing examples of fully explained solutions. 


Parameters of the program
Name of program:

EMSolution_Algebra_short

Number of problems:

35126

Number of similar variants:

3

Languages of interface:

English, German

Price:

71 EUR

Size of archive:

4045 kb

35254 algebraic problems. Algebra 1 and Algebra 2 levels. Fully explained stepbystep solutions and proofs. Transformation, simplification and evaluation of rational expressions. Proofs of identities. Solutions of equations. Solutions of inequalities. Linear, quadratic, cubic, reciprocal, highdegree and fractional expressions. Related theory. Option of translation. Sorting problems by topics, complexity levels and solution methods. Authoring options enabling development of tests, quizzes, exams and problem solving lesson plans. Automatic generation of variant tests. Dozens of ready tests.
System Requirements:
Pentium 2 or higher
64 MB RAM
Windows 98 or higher
Internet Explorer 5.5 or higher
Plugin MathPlayer (downloadable from here)
Program's detail
Examples
An online sample of math problems and problem solutions from this program is provided below:
EMTEACHLINE MATHEMATICS SOFTWARE: MATH PROBLEM SOLVING FOR KIDS AND TEENS
Press release
ABSTRACT. EMTeachline Software has released a PCbased mathematics software package that offers a huge collection of problemsolving lessons in arithmetic, prealgebra, algebra, trigonometry and hyperbolic trigonometry with handson tutorials. This encyclopedic software contains hundreds of thousands of fully explained step by step solutions to math problems from basic to advanced and thousands of related definitions, rules, math formulas and theorems. Each step of solution is provided with its objective, relevant definition and rule, and with fully explained step by step proof of the underlying math formulae or theorem. The software helps children review, explore and effectively learn essential math skills. Easytouse test authoring tools enable math teachers to develop customizable math tests, variant tests, quizzes, exams and problemsolving lesson plans. The software is suitable for elementary, middle and high school use. Designed as a supplement classroom instruction. Provides a useful help for math teachers.
1. SOFTWARE OVERVIEW
Building problem solving skills in math requires grasping math concepts and a large amount of training in solving similar tasks. EMTeachline Mathematics Software provides children with the chance to do just that. This software encourages kids to learn through indepth understanding of each solution step and repetition rather than through rote memorization. Children who are struggling in math learn best through repetition. Those who stick with this mathematics software will come away with a stronger understanding of fundamental math concepts, improved higherlevel thinking skills and excellent skills in solving math problems.
EMTeachline Mathematics Problem Solving Software  EMSolution  consists of dozens of modules arranged in topics. Each module offers hundreds of math problem types, with dozens of similar math problems within one type. Math learning is effective when problems gradually advance in difficulty. This software offers 11 levels of complexity for each problem type, from basic to extra difficult. Kids who are strong in math and need a challenge can adjust the difficulty level at any moment.
Learners can review solutions step by step and study related math theory. Each step of solution is provided with its objective, relevant definition and rule, and with fully explained step by step proof of the underlying math formulae or theorem. This tutoring material is provided in a useful manner, so that it is always under hand. A set of ready math tests is designed for children to review and reinforce their math skills. Problem situations, solutions and tutoring material can be printed out.
More than just a math tutorial, this bilingual problemsolving software offers a way for children to learn math lexicon in a foreign language. Translation of any text to German (or another language) is easily obtained by doubleclicking on it. Those who study not in a native language will find this option particularly attractive.
Test authoring options make development of math tests, quizzes, homeworks and exams an easy and creative work. With thousands math problems at hands, math teachers do not have to search for fresh exmples. You can select math problems by complexity levels, solution methods and types of tasks; develop customizable math tests of varied complexity in a minute; create your own didactic materials and problemsolving lesson plans, and generate numerous similar variant tests around a constructed example. All developed materials can be printed out or stored in a file and reused. These easytouse authoring tools provide an ideal solution for a classroom teacher.
Let's be honest  this program is not for funseekers. No sounds, no colorful visual effects. The tutorial material is presented in a dry academic fashion. Most kids would use this program to review for an exam that they are required to take. However, the contents hold much appeal for children who enjoy solving math problems and like challenges. Those who look for a systematic math knowledge will find the software to be particularly engaging.
2. SKILLS COVERED
Arithmetic and PreAlgebra: Operations: multiplication, division, addition, subtraction. Fractions, powers. Numeric expressions: estimation, equivalencies, problemsolving. Solving arithmetic problems using algebraic formulas.
Algebra: Polynomial and fractional rational expressions: transformation, simplification, evaluation. Solution of linear, quadratic, cubic, biquadratic, reciprocal and fractional algebraic equations and inequalities. Proofs of algebraic identities. Solution methods: Substitution, factoring, grouping, Bezout theorem, formulas of short multiplication, method of intervals and more. Related theory: definitions and rules, proof of algebraic formulas and theorems.
Trigonometry and Hyperbolic Trigonometry: trigonometric and hyperbolic functions, arcus functions. Trigonometric and hyperbolic expressions: transformation, simplification, evaluation. Solution of trigonometric and hyperbolic equations. Proofs of trigonometric and hyperbolic identities. Solution methods: universal substitution, sum, product and addition of trigonometric functions, power reduction, multiple argument, shift of argument and more. Related theory: definitions and rules, proof of trigonometric and hyperbolic formulas.
3. USER OPTIONS
For math students: You can review solutions of math problems step by step, learn related math concepts, study solution methods, review proofs of used math formulas, try to solve similar math problems on your own, and in parallel, learn math lexicon in a foreign language!
For math teachers: You can use an extensive bank of math problems; arrange problems by topic, complexity level, solution method and type of task; compile math tests, quizzes, homeworks and exams of varied complexity; create your own didactic materials and problemsolving lesson plans; generate numerous similar variant math tests around a constructed example. You can use dozens of ready variant tests.
Contents of the program
Themes
Chapters and sections
Rational expressions. Computational problems 
Chapters 
Sections 
Evaluation of linear expressions and expressions reduced to them

 Evaluation of linear expressions and expressions reduced to them. Elementary linear expressions. Evaluation
 Evaluation of linear expressions and expressions reduced to them. Elementary linear expressions containing fractions. Evaluation
 Evaluation of linear expressions and expressions reduced to them. Linear expressions. Distributive law. Evaluation
 Evaluation of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication. Evaluation
 Evaluation of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication. Cubes. Evaluation
 Evaluation of linear expressions and expressions reduced to them. Linear expressions. Properties of powers. Evaluation
 Evaluation of linear expressions and expressions reduced to them. Expressions reduced to linear expressions. Evaluation
 Evaluation of linear expressions and expressions reduced to them. Fractional expressions reduced to linear expressions. Evaluation
 Evaluation of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Rational coefficients. Evaluation
 Evaluation of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Integer coefficients. Evaluation
 Evaluation of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Integer coefficients. Evaluation
 Evaluation of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Rational coefficients. Evaluation
 Evaluation of linear expressions and expressions reduced to them. Linear expressions. Factorization of quadratic trinomial. Evaluation
 Evaluation of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Distributive law. Evaluation
 Evaluation of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Formulas of short multiplication. Evaluation
 Evaluation of linear expressions and expressions reduced to them. Linear expressions. Properties of fractions. Distributive law. Evaluation
 Evaluation of linear expressions and expressions reduced to them. Linear expressions. Properties of fractions. Formulas of short multiplication. Evaluation

Evaluation of quadratic expressions and expressions reduced to them

 Evaluation of quadratic expressions and expressions reduced to them. Elementary quadratic expressions. Evaluation
 Evaluation of quadratic expressions and expressions reduced to them. Quadratic expressions containing fractions. Evaluation
 Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Distributive law. Integer coefficients. Evaluation
 Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Formulas of short multiplication. Evaluation
 Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Distributive law. Rational coefficients. Evaluation
 Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Factorization of quadratic trinomial. Evaluation
 Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Properties of powers. Evaluation
 Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Grouping method. Evaluation
 Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Method of substitution. Distributive law. Integer coefficients. Evaluation
 Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Method of substitution. Distributive law. Rational coefficients. Evaluation
 Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Method of substitution. Formulas of short multiplication. Integer coefficients. Evaluation
 Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Method of substitution. Formulas of short multiplication. Rational coefficients. Evaluation
 Evaluation of quadratic expressions and expressions reduced to them. Expressions reduced to quadratic. Method of substitution. Factorization of quadratic trinomial. Evaluation

Evaluation of algebraic highdegree expressions

 Evaluation of algebraic highdegree expressions. Algebraic highdegree expressions. Bezout theorem. Integer roots. Evaluation
 Evaluation of algebraic highdegree expressions. Algebraic highdegree expressions. Bezout theorem. Irrational roots. Evaluation
 Evaluation of algebraic highdegree expressions. Algebraic highdegree expressions. Bezout theorem. Integer roots. Evaluation
 Evaluation of algebraic highdegree expressions. Algebraic highdegree expressions. Grouping method. Evaluation
 Evaluation of algebraic highdegree expressions. Algebraic highdegree expressions. Perfect square. Evaluation
 Evaluation of algebraic highdegree expressions. Algebraic highdegree expressions. Bezout theorem. Irrational roots. Evaluation
 Evaluation of algebraic highdegree expressions. Algebraic highdegree expressions. Formulas of short multiplication. Evaluation
 Evaluation of algebraic highdegree expressions. Algebraic highdegree expressions. Difference of squares. Evaluation
 Evaluation of algebraic highdegree expressions. Algebraic highdegree expressions. Factorization of quadratic trinomial. Evaluation
 Evaluation of algebraic highdegree expressions. Algebraic highdegree expressions. Properties of fractions. Evaluation
 Evaluation of algebraic highdegree expressions. Algebraic highdegree expressions. Difference and sum of cubes. Evaluation

Evaluation of fractional algebraic expressions

 Evaluation of fractional algebraic expressions. Elementary fractional algebraic expressions. Evaluation
 Evaluation of fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with linear expression in numerator. Evaluation
 Evaluation of fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with quadratic expression in numerator. Evaluation
 Evaluation of fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with cubic expression in numerator. Evaluation
 Evaluation of fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with biquadratic expression in numerator. Evaluation
 Evaluation of fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with reciprocal expression in numerator. Evaluation

Comparison of values of linear expressions and expressions reduced to them

 Comparison of values of linear expressions and expressions reduced to them. Elementary linear inequalities
 Comparison of values of linear expressions and expressions reduced to them. Elementary linear inequalities containing fractions
 Comparison of values of linear expressions and expressions reduced to them. Linear inequalities. Distributive law
 Comparison of values of linear expressions and expressions reduced to them. Linear inequalities. Formulas of short multiplication
 Comparison of values of linear expressions and expressions reduced to them. Linear inequalities. Formulas of short multiplication. Cubes. Comparison of values
 Comparison of values of linear expressions and expressions reduced to them. Linear inequalities. Properties of powers. Comparison of values
 Comparison of values of linear expressions and expressions reduced to them. Inequalities reduced to linear inequalities. Comparison of values
 Comparison of values of linear expressions and expressions reduced to them. Fractional inequalities. Properties of fractions. Rational coefficients. Comparison of values
 Comparison of values of linear expressions and expressions reduced to them. Fractional inequalities. Properties of fractions. Integer coefficients. Comparison of values
 Comparison of values of linear expressions and expressions reduced to them. Fractional inequalities. Method of substitution. Integer coefficients. Comparison of values
 Comparison of values of linear expressions and expressions reduced to them. Fractional inequalities. Method of substitution. Rational coefficients. Comparison of values
 Comparison of values of linear expressions and expressions reduced to them. Linear inequalities. Factorization of quadratic trinomial. Comparison of values
 Comparison of values of linear expressions and expressions reduced to them. Linear inequalities. Method of substitution. Distributive law. Comparison of values
 Comparison of values of linear expressions and expressions reduced to them. Linear inequalities. Method of substitution. Formulas of short multiplication. Comparison of values
 Comparison of values of linear expressions and expressions reduced to them. Linear inequalities. Properties of fractions. Distributive law. Comparison of values
 Comparison of values of linear expressions and expressions reduced to them. Linear inequalities. Properties of fractions. Formulas of short multiplication. Comparison of values

Comparison of values of quadratic expressions and expressions reduced to them

 Comparison of values of quadratic expressions and expressions reduced to them. Elementary quadratic expressions. Comparison
 Comparison of values of quadratic expressions and expressions reduced to them. Compare quadratic expressions containing fractions
 Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Distributive law. Integer coefficients
 Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Formulas of short multiplication
 Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Distributive law. Rational coefficients
 Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Factorization of quadratic trinomial
 Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Properties of powers
 Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Grouping method
 Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Method of substitution. Distributive law. Integer coefficients
 Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Method of substitution. Distributive law. Rational coefficients
 Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Method of substitution. Formulas of short multiplication. Integer coefficients
 Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Method of substitution. Formulas of short multiplication. Rational coefficients
 Comparison of values of quadratic expressions and expressions reduced to them. Compare expressions reduced to quadratic. Method of substitution. Factorization of quadratic trinomial

Comparison of values of algebraic highdegree expressions

 Comparison of values of algebraic highdegree expressions. Compare algebraic highdegree expressions. Bezout theorem. Irrational roots
 Comparison of values of algebraic highdegree expressions. Compare algebraic highdegree expressions. Bezout theorem. Integer roots
 Comparison of values of algebraic highdegree expressions. Compare algebraic highdegree expressions. Grouping method
 Comparison of values of algebraic highdegree expressions. Compare algebraic highdegree expressions. Perfect square
 Comparison of values of algebraic highdegree expressions. Compare algebraic highdegree expressions. Formulas of short multiplication
 Comparison of values of algebraic highdegree expressions. Compare algebraic highdegree expressions. Difference of squares
 Comparison of values of algebraic highdegree expressions. Compare algebraic highdegree expressions. Factorization of quadratic trinomial
 Comparison of values of algebraic highdegree expressions. Compare algebraic highdegree expressions. Properties of fractions
 Comparison of values of algebraic highdegree expressions. Compare algebraic highdegree expressions. Difference and sum of cubes

Comparison of values of fractional algebraic expressions

 Comparison of values of fractional algebraic expressions. Compare fractional algebraic expressions reduced to a fraction with linear expression in numerator
 Comparison of values of fractional algebraic expressions. Compare fractional algebraic expressions reduced to a fraction with quadratic expression in numerator
 Comparison of values of fractional algebraic expressions. Compare fractional algebraic expressions reduced to a fraction with cubic expression in numerator
 Comparison of values of fractional algebraic expressions. Compare fractional algebraic expressions reduced to a fraction with reciprocal expression in numerator

Rational expressions. Transformations and proofs 
Chapters 
Sections 
Transformation of linear expressions and expressions reduced to them

 Transformation of linear expressions and expressions reduced to them. Elementary linear expressions
 Transformation of linear expressions and expressions reduced to them. Elementary linear expressions containing fractions
 Transformation of linear expressions and expressions reduced to them. Linear expressions. Distributive law
 Transformation of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication
 Transformation of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication. Cubes
 Transformation of linear expressions and expressions reduced to them. Linear expressions. Properties of powers
 Transformation of linear expressions and expressions reduced to them. Expressions reduced to linear expressions
 Transformation of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Rational coefficients
 Transformation of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Integer coefficients
 Transformation of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Integer coefficients
 Transformation of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Rational coefficients
 Transformation of linear expressions and expressions reduced to them. Linear expressions. Factorization of quadratic trinomial
 Transformation of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Distributive law
 Transformation of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Formulas of short multiplication

Transformation of quadratic algebraic expressions and expressions reduced to them

 Transformation of quadratic algebraic expressions and expressions reduced to them. Elementary quadratic expressions
 Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions containing fractions
 Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Integer coefficients
 Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Formulas of short multiplication
 Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Rational coefficients
 Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Decomposition of quadratic trinomial
 Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Properties of powers
 Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Grouping method
 Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Integer coefficients
 Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Rational coefficients
 Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Integer coefficients
 Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Rational coefficients
 Transformation of quadratic algebraic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Factorization of quadratic trinomial
 Transformation of quadratic algebraic expressions and expressions reduced to them. Fractional expressions. Method of substitution. Distributive law. Integer coefficients

Transformation of algebraic highdegree expressions

 Transformation of algebraic highdegree expressions. High degrees. Bezout theorem. Standard problems. Integer roots
 Transformation of algebraic highdegree expressions. High degrees. Bezout theorem. Irrational roots
 Transformation of algebraic highdegree expressions. High degrees. Bezout theorem. Reducible problems. Integer roots
 Transformation of algebraic highdegree expressions. High degrees. Grouping method
 Transformation of algebraic highdegree expressions. High degrees. Perfect square
 Transformation of algebraic highdegree expressions. High degrees. Bezout theorem. Reducible problems. Irrational roots
 Transformation of algebraic highdegree expressions. High degrees. Formulas of short multiplication
 Transformation of algebraic highdegree expressions. High degrees. Difference of squares
 Transformation of algebraic highdegree expressions. High degrees. Factorization of quadratic trinomial
 Transformation of algebraic highdegree expressions. High degrees. Properties of fractions
 Transformation of algebraic highdegree expressions. High degrees. Difference and sum of cubes

Transformation of fractional algebraic expressions

 Transformation of fractional algebraic expressions. Elementary fractional algebraic expressions
 Transformation of fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with linear expression in numerator
 Transformation of fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with quadratic expression in numerator
 Transformation of fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with cubic expression in numerator
 Transformation of fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with biquadratic expression in numerator
 Transformation of fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with reciprocal expression in numerator
 Transformation of fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with reciprocal expression in numerator. Method of substitution

Factorization of linear expressions and expressions reduced to them

 Factorization of linear expressions and expressions reduced to them. Elementary linear expressions
 Factorization of linear expressions and expressions reduced to them. Elementary linear expressions containing fractions
 Factorization of linear expressions and expressions reduced to them. Linear expressions. Distributive law
 Factorization of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication
 Factorization of linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication. Cubes
 Factorization of linear expressions and expressions reduced to them. Linear expressions. Properties of powers
 Factorization of linear expressions and expressions reduced to them. Expressions reduced to linear expressions
 Factorization of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Rational coefficients
 Factorization of linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Integer coefficients
 Factorization of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Integer coefficients
 Factorization of linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Rational coefficients
 Factorization of linear expressions and expressions reduced to them. Linear expressions. Factorization of quadratic trinomial
 Factorization of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Distributive law
 Factorization of linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Formulas of short multiplication

Factorization of quadratic expressions and expressions reduced to them

 Factorization of quadratic expressions and expressions reduced to them. Elementary quadratic expressions
 Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions containing fractions
 Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Integer coefficients
 Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Formulas of short multiplication
 Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Rational coefficients
 Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Factorization of quadratic trinomial
 Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Properties of powers
 Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Grouping method
 Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Integer coefficients
 Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Rational coefficients
 Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Integer coefficients
 Factorization of quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Rational coefficients

Factorization of algebraic highdegree expressions

 Factorization of algebraic highdegree expressions. High degrees. Grouping method
 Factorization of algebraic highdegree expressions. High degrees. Perfect square
 Factorization of algebraic highdegree expressions. High degrees. Formulas of short multiplication
 Factorization of algebraic highdegree expressions. High degrees. Difference of squares
 Factorization of algebraic highdegree expressions. High degrees. Factorization of quadratic trinomial
 Factorization of algebraic highdegree expressions. High degrees. Properties of fractions
 Factorization of algebraic highdegree expressions. High degrees. Difference and sum of cubes

Proof of identity. Linear expressions and expressions reduced to them

 Proof of identity. Linear expressions and expressions reduced to them. Elementary linear expressions
 Proof of identity. Linear expressions and expressions reduced to them. Elementary linear expressions containing fractions
 Proof of identity. Linear expressions and expressions reduced to them. Linear expressions. Distributive law
 Proof of identity. Linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication
 Proof of identity. Linear expressions and expressions reduced to them. Linear expressions. Formulas of short multiplication. Cubes
 Proof of identity. Linear expressions and expressions reduced to them. Linear expressions. Properties of powers
 Proof of identity. Linear expressions and expressions reduced to them. Expressions reduced to linear expressions
 Proof of identity. Linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Rational coefficients
 Proof of identity. Linear expressions and expressions reduced to them. Fractional expressions. Properties of fractions. Integer coefficients
 Proof of identity. Linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Integer coefficients
 Proof of identity. Linear expressions and expressions reduced to them. Fractional expressions. Method of substitution. Rational coefficients
 Proof of identity. Linear expressions and expressions reduced to them. Linear expressions. Factorization of quadratic trinomial
 Proof of identity. Linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Distributive law
 Proof of identity. Linear expressions and expressions reduced to them. Linear expressions. Method of substitution. Formulas of short multiplication
 Proof of identity. Linear expressions and expressions reduced to them. Linear expressions. Properties of fractions. Distributive law

Proof of identity. Quadratic expressions and expressions reduced to them

 Proof of identity. Quadratic expressions and expressions reduced to them. Elementary quadratic expressions
 Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions containing fractions
 Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Integer coefficients
 Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions. Formulas of short multiplication
 Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions. Distributive law. Rational coefficients
 Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions. Factorization of quadratic trinomial
 Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions. Properties of powers
 Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions. Grouping method
 Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Integer coefficients
 Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Distributive law. Rational coefficients
 Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Integer coefficients
 Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Formulas of short multiplication. Rational coefficients
 Proof of identity. Quadratic expressions and expressions reduced to them. Quadratic expressions. Method of substitution. Grouping method
 Proof of identity. Quadratic expressions and expressions reduced to them. Fractional expressions. Method of substitution. Distributive law. Integer coefficients
 Proof of identity. Quadratic expressions and expressions reduced to them. Fractional expressions. Method of substitution. Distributive law. Rational coefficients

Proof of identity. Highdegree expressions

 Proof of identity. Highdegree expressions. High degrees. Bezout theorem. Standard problems. Integer roots
 Proof of identity. Highdegree expressions. High degrees. Bezout theorem. Irrational roots
 Proof of identity. Highdegree expressions. High degrees. Bezout theorem. Reducible problems. Integer roots
 Proof of identity. Highdegree expressions. High degrees. Grouping method
 Proof of identity. Highdegree expressions. High degrees. Perfect square
 Proof of identity. Highdegree expressions. High degrees. Bezout theorem. Reducible problems. Irrational roots
 Proof of identity. Highdegree expressions. High degrees. Formulas of short multiplication
 Proof of identity. Highdegree expressions. High degrees. Difference of squares
 Proof of identity. Highdegree expressions. High degrees. Properties of fractions

Proof of identity. Fractional algebraic expressions

 Proof of identity. Fractional algebraic expressions. Elementary fractional algebraic expressions
 Proof of identity. Fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with linear expression in numerator
 Proof of identity. Fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with quadratic expression in numerator
 Proof of identity. Fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with cubic expression in numerator
 Proof of identity. Fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with biquadratic expression in numerator

Rational expressions. Proofs of inequalities 
Chapters 
Sections 
Proof of strict inequalities. Linear expressions and expressions reduced to them

 Proof of strict inequalities. Linear expressions and expressions reduced to them. Elementary linear inequalities
 Proof of strict inequalities. Linear expressions and expressions reduced to them. Elementary linear inequalities containing fractions
 Proof of strict inequalities. Linear expressions and expressions reduced to them. Linear inequalities. Distributive law
 Proof of strict inequalities. Linear expressions and expressions reduced to them. Linear inequalities. Formulas of short multiplication
 Proof of strict inequalities. Linear expressions and expressions reduced to them. Linear inequalities. Formulas of short multiplication. Cubes
 Proof of strict inequalities. Linear expressions and expressions reduced to them. Linear inequalities. Properties of powers
 Proof of strict inequalities. Linear expressions and expressions reduced to them. Inequalities reduced to linear inequalities
 Proof of strict inequalities. Linear expressions and expressions reduced to them. Fractional inequalities. Properties of fractions. Rational coefficients
 Proof of strict inequalities. Linear expressions and expressions reduced to them. Fractional inequalities. Properties of fractions. Integer coefficients
 Proof of strict inequalities. Linear expressions and expressions reduced to them. Fractional inequalities. Method of substitution. Integer coefficients
 Proof of strict inequalities. Linear expressions and expressions reduced to them. Fractional inequalities. Method of substitution. Rational coefficients
 Proof of strict inequalities. Linear expressions and expressions reduced to them. Linear inequalities. Factorization of quadratic trinomial
 Proof of strict inequalities. Linear expressions and expressions reduced to them. Linear inequalities. Method of substitution. Distributive law
 Proof of strict inequalities. Linear expressions and expressions reduced to them. Linear inequalities. Method of substitution. Formulas of short multiplication
 Proof of strict inequalities. Linear expressions and expressions reduced to them. Linear inequalities. Method of substitution. Properties of powers

Proof of strict inequalities. Quadratic expressions

 Proof of strict inequalities. Quadratic expressions. Elementary quadratic inequalities
 Proof of strict inequalities. Quadratic expressions. Quadratic inequalities containing fractions
 Proof of strict inequalities. Quadratic expressions. Quadratic inequalities. Distributive law. Integer coefficients
 Proof of strict inequalities. Quadratic expressions. Quadratic inequalities. Grouping method
 Proof of strict inequalities. Quadratic expressions. Quadratic inequalities. Method of substitution. Distributive law. Integer coefficients
 Proof of strict inequalities. Quadratic expressions. Quadratic inequalities. Method of substitution. Distributive law. Rational coefficients
 Proof of strict inequalities. Quadratic expressions. Quadratic inequalities. Method of substitution. Formulas of short multiplication. Integer coefficients
 Proof of strict inequalities. Quadratic expressions. Quadratic inequalities. Method of substitution. Formulas of short multiplication. Rational coefficients
 Proof of strict inequalities. Quadratic expressions. Quadratic inequalities. Method of substitution. Grouping method
 Proof of strict inequalities. Quadratic expressions. Quadratic inequalities. Method of substitution. Factorization of quadratic trinomial
 Proof of strict inequalities. Quadratic expressions. Fractional inequalities. Method of substitution. Distributive law. Integer coefficients

Proof of strict inequalities. Algebraic highdegree expressions

 Proof of strict inequalities. Algebraic highdegree expressions. High degrees. Bezout theorem. Standard problems. Integer roots
 Proof of strict inequalities. Algebraic highdegree expressions. High degrees. Bezout theorem. Reducible problems

Proof of strict inequalities. Fractional algebraic expressions

 Proof of strict inequalities. Fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with linear expression in numerator. To prove inequality
 Proof of strict inequalities. Fractional algebraic expressions. Fractional algebraic expressions reduced to a fraction with quadratic expression in numerator. To prove inequality

Rational equations 
Chapters 
Sections 
Linear equations

 Linear equations. Elementary linear equations
 Linear equations. Linear equations containing fractions
 Linear equations. Linear equations. Distributive law
 Linear equations. Equations reduced to linear equations. Formulas of short multiplication
 Linear equations. Linear equations. Formulas of short multiplication. Cubes
 Linear equations. Linear equations. Properties of powers
 Linear equations. Equations reduced to linear equations
 Linear equations. Homographic equations with rational coefficients. Properties of fractions
 Linear equations. Homographic equations with integer coefficients. Properties of fractions
 Linear equations. Homographic equations with integer coefficients. Method of substitution
 Linear equations. Homographic equations with rational coefficients. Method of substitution
 Linear equations. Linear equations. Factorization of quadratic trinomial
 Linear equations. Equations reduced to linear. Method of substitution. Distributive law
 Linear equations. Equations reduced to linear. Method of substitution. Distributive law. Formulas of short multiplication

Quadratic equations

 Quadratic equations. Elementary quadratic equations
 Quadratic equations. Quadratic equations containing fractions
 Quadratic equations. Equations with integer coefficients. Distributive law
 Quadratic equations. Quadratic equations. Formulas of short multiplication
 Quadratic equations. Quadratic equations with rational coefficients. Distributive law
 Quadratic equations. Equations reduced to quadratic. Factorization of quadratic trinomial
 Quadratic equations. Equations reduced to quadratic. Properties of powers
 Quadratic equations. Fractional algebraic equations reduced to quadratic equations. Distributive law
 Quadratic equations. Equations. Grouping method
 Quadratic equations. Equations. Method of substitution. Distributive law. Integer coefficients
 Quadratic equations. Equations. Method of substitution. Distributive law. Rational coefficients
 Quadratic equations. Equations. Method of substitution. Formulas of short multiplication
 Quadratic equations. Equations. Method of substitution. Properties of fractions
 Quadratic equations. Equations. Method of substitution. Grouping method
 Quadratic equations. Equations. Method of substitution. Factorization of quadratic trinomial
 Quadratic equations. Fractional equations. Method of substitution. Distributive law
 Quadratic equations. Fractional equations reduced to quadratic equations. Method of substitution
 Quadratic equations. Fractional equations. Method of substitution. Formulas of short multiplication
 Quadratic equations. Fractional algebraic equations reduced to quadratic equations. Formulas of short multiplication

Cubic equations

 Cubic equations. Cubic equations in reduced form
 Cubic equations. Cubic equations in general form

Algebraic equations. Method of substitution

 Algebraic equations. Method of substitution. Elementary biquadratic equations
 Algebraic equations. Method of substitution. Algebraic equations reduced to biquadratic equations
 Algebraic equations. Method of substitution. Algebraic equations. Linear substitution
 Algebraic equations. Method of substitution. Algebraic equations. Quadratic substitution
 Algebraic equations. Method of substitution. Algebraic equations. Homographic substitution
 Algebraic equations. Method of substitution. Reciprocal equations
 Algebraic equations. Method of substitution. Algebraic equations reduced to reciprocal

Algebraic highdegree equations

 Algebraic highdegree equations. Highdegree equations. Bezout theorem. Integer roots
 Algebraic highdegree equations. Highdegree equations. Bezout theorem. Irrational roots
 Algebraic highdegree equations. Highdegree equations reduced to the form allowing application of the Bezout theorem. Integer roots
 Algebraic highdegree equations. Highdegree equations. Grouping method
 Algebraic highdegree equations. Highdegree equations. Perfect square
 Algebraic highdegree equations. Highdegree equations reduced to the form allowing application of the Bezout theorem. Irrational roots
 Algebraic highdegree equations. Highdegree equations. Formulas of short multiplication
 Algebraic highdegree equations. Highdegree equations. Difference of squares
 Algebraic highdegree equations. Highdegree equations. Factorization of quadratic trinomial
 Algebraic highdegree equations. Highdegree equations. Properties of fractions
 Algebraic highdegree equations. Highdegree equations. Difference and sum of cubes
 Algebraic highdegree equations. Highdegree equations. Method of substitution

Fractional algebraic equations

 Fractional algebraic equations. Elementary fractional algebraic equations
 Fractional algebraic equations. Fractional algebraic equations reduced to linear equations
 Fractional algebraic equations. Fractional algebraic equations reduced to quadratic equations
 Fractional algebraic equations. Fractional algebraic equations reduced to cubic equations
 Fractional algebraic equations. Fractional algebraic equations reduced to biquadratic equations
 Fractional algebraic equations. Fractional algebraic equations reduced to reciprocal equations
 Fractional algebraic equations. Fractional algebraic equations reduced to quadratic equations. Method of substitution
 Fractional algebraic equations. Fractional algebraic equations. Method of substitution

Rational inequalities 
Chapters 
Sections 
Weak linear inequalities

 Weak linear inequalities. Elementary linear weak inequalities
 Weak linear inequalities. Linear weak inequalities containing fractions
 Weak linear inequalities. Homographic weak inequalities. Method of substitution. Rational coefficients
 Weak linear inequalities. Linear weak inequalities. Distributive law
 Weak linear inequalities. Weak inequalities reduced to linear inequalities. Formulas of short multiplication
 Weak linear inequalities. Linear weak inequalities. Formulas of short multiplication. Cubes
 Weak linear inequalities. Linear weak inequalities. Properties of fractions
 Weak linear inequalities. Linear weak inequalities. Factorization of quadratic trinomial
 Weak linear inequalities. Weak inequalities reduced to linear inequalities. Method of substitution. Distributive law
 Weak linear inequalities. Weak inequalities reduced to linear inequalities. Method of substitution. Formulas of short multiplication
 Weak linear inequalities. Weak inequalities reduced to linear inequalities. Method of substitution. Properties of powers
 Weak linear inequalities. Linear weak inequalities. Properties of powers
 Weak linear inequalities. Weak inequalities reduced to linear inequalities
 Weak linear inequalities. Fractional weak inequalities reduced to linear inequalities
 Weak linear inequalities. Homographic weak inequalities. Properties of fractions. Rational coefficients
 Weak linear inequalities. Homographic weak inequalities. Properties of fractions. Integer coefficients
 Weak linear inequalities. Homographic weak inequalities. Method of substitution. Integer coefficients
 Weak linear inequalities. Weak inequalities reduced to linear inequalities. Method of substitution. Factorization of quadratic trinomial
 Weak linear inequalities. Weak inequalities reduced to linear inequalities. Properties of fractions. Distributive law
 Weak linear inequalities. Weak inequalities reduced to linear inequalities. Properties of fractions. Formulas of short multiplication
 Weak linear inequalities. Weak inequalities reduced to linear inequalities. Properties of fractions. Properties of powers
 Weak linear inequalities. Weak inequalities reduced to linear inequalities. Properties of fractions. Factorization of quadratic trinomial

Strict linear inequalities

 Strict linear inequalities. Elementary strict linear inequalities
 Strict linear inequalities. Strict linear inequalities containing fractions
 Strict linear inequalities. Strict linear inequalities. Distributive law
 Strict linear inequalities. Strict inequalities reduced to linear inequalities. Formulas of short multiplication
 Strict linear inequalities. Strict inequalities reduced to linear inequalities. Formulas of short multiplication. Cubes
 Strict linear inequalities. Strict linear inequalities. Properties of fractions
 Strict linear inequalities. Strict linear inequalities. Properties of powers
 Strict linear inequalities. Strict inequalities reduced to linear inequalities
 Strict linear inequalities. Strict fractional inequalities reduced to linear inequalities
 Strict linear inequalities. Strict homographic inequalities. Properties of fractions. Rational coefficients
 Strict linear inequalities. Strict homographic inequalities. Properties of fractions. Integer coefficients
 Strict linear inequalities. Strict homographic inequalities. Method of substitution. Integer coefficients
 Strict linear inequalities. Strict homographic inequalities. Method of substitution. Rational coefficients
 Strict linear inequalities. Strict linear inequalities. Factorization of quadratic trinomial
 Strict linear inequalities. Strict inequalities reduced to linear inequalities. Method of substitution. Distributive law
 Strict linear inequalities. Strict inequalities reduced to linear inequalities. Method of substitution. Formulas of short multiplication
 Strict linear inequalities. Strict inequalities reduced to linear inequalities. Method of substitution. Properties of powers
 Strict linear inequalities. Strict inequalities reduced to linear inequalities. Method of substitution. Factorization of quadratic trinomial
 Strict linear inequalities. Strict inequalities reduced to linear inequalities. Properties of fractions. Distributive law
 Strict linear inequalities. Strict inequalities reduced to linear inequalities. Properties of fractions. Formulas of short multiplication
 Strict linear inequalities. Strict inequalities reduced to linear inequalities. Properties of fractions. Properties of powers
 Strict linear inequalities. Strict inequalities reduced to linear inequalities. Properties of fractions. Factorization of quadratic trinomial

Strict quadratic inequalities

 Strict quadratic inequalities. Elementary quadratic strict inequalities
 Strict quadratic inequalities. Quadratic strict inequalities containing fractions
 Strict quadratic inequalities. Strict inequalities. Method of substitution. Formulas of short multiplication. Integer coefficients
 Strict quadratic inequalities. Strict inequalities. Method of substitution. Distributive law. Rational coefficients
 Strict quadratic inequalities. Strict inequalities. Distributive law. Integer coefficients
 Strict quadratic inequalities. Strict inequalities. Formulas of short multiplication
 Strict quadratic inequalities. Strict inequalities. Distributive law. Rational coefficients
 Strict quadratic inequalities. Strict inequalities. Factorization of quadratic trinomial
 Strict quadratic inequalities. Strict inequalities. Properties of powers
 Strict quadratic inequalities. Fractional strict algebraic inequalities reduced to quadratic inequalities
 Strict quadratic inequalities. Strict inequalities. Grouping method
 Strict quadratic inequalities. Strict inequalities. Method of substitution. Distributive law. Integer coefficients
 Strict quadratic inequalities. Strict inequalities. Method of substitution. Formulas of short multiplication. Rational coefficients
 Strict quadratic inequalities. Fractional strict inequalities. Method of substitution. Distributive law. Integer coefficients
 Strict quadratic inequalities. Fractional strict inequalities. Method of substitution. Distributive law. Rational coefficients
 Strict quadratic inequalities. Fractional strict inequalities. Method of substitution. Formulas of short multiplication. Integer coefficients
 Strict quadratic inequalities. Fractional strict inequalities. Method of substitution. Formulas of short multiplication. Rational coefficients

Weak quadratic inequalities

 Weak quadratic inequalities. Elementary quadratic weak inequalities
 Weak quadratic inequalities. Quadratic weak inequalities containing fractions
 Weak quadratic inequalities. Weak inequalities. Distributive law. Integer coefficients
 Weak quadratic inequalities. Weak inequalities. Formulas of short multiplication
 Weak quadratic inequalities. Weak inequalities. Distributive law. Rational coefficients
 Weak quadratic inequalities. Weak inequalities. Factorization of quadratic trinomial
 Weak quadratic inequalities. Weak inequalities. Properties of powers
 Weak quadratic inequalities. Fractional algebraic weak inequalities reduced to quadratic inequalities
 Weak quadratic inequalities. Weak inequalities. Grouping method
 Weak quadratic inequalities. Weak inequalities. Method of substitution. Distributive law. Integer coefficients
 Weak quadratic inequalities. Weak inequalities. Method of substitution. Distributive law. Rational coefficients
 Weak quadratic inequalities. Weak inequalities. Method of substitution. Formulas of short multiplication. Integer coefficients
 Weak quadratic inequalities. Weak inequalities. Method of substitution. Formulas of short multiplication. Rational coefficients
 Weak quadratic inequalities. Fractional weak inequalities. Method of substitution. Distributive law. Integer coefficients
 Weak quadratic inequalities. Fractional weak inequalities. Method of substitution. Distributive law. Rational coefficients
 Weak quadratic inequalities. Fractional weak inequalities. Method of substitution. Formulas of short multiplication. Integer coefficients
 Weak quadratic inequalities. Fractional weak inequalities. Method of substitution. Formulas of short multiplication. Rational coefficients

Strict algebraic highdegree inequalities

 Strict algebraic highdegree inequalities. Strict highdegree inequalities. Bezout theorem. Integer roots
 Strict algebraic highdegree inequalities. Strict highdegree inequalities. Bezout theorem. Irrational roots
 Strict algebraic highdegree inequalities. Strict highdegree inequalities. Bezout theorem. Integer roots
 Strict algebraic highdegree inequalities. Strict highdegree inequalities. Grouping method
 Strict algebraic highdegree inequalities. Strict highdegree inequalities. Perfect square
 Strict algebraic highdegree inequalities. Strict inequalities. Formulas of short multiplication
 Strict algebraic highdegree inequalities. Strict inequalities. Difference of squares
 Strict algebraic highdegree inequalities. Strict inequalities. Factorization of quadratic trinomial
 Strict algebraic highdegree inequalities. Strict inequalities. Properties of fractions
 Strict algebraic highdegree inequalities. Strict inequalities. Difference and sum of cubes

Weak algebraic highdegree inequalities

 Weak algebraic highdegree inequalities. Weak highdegree inequalities. Bezout theorem. Integer roots
 Weak algebraic highdegree inequalities. Weak highdegree inequalities. Bezout theorem. Irrational roots
 Weak algebraic highdegree inequalities. Weak highdegree inequalities. Bezout theorem. Integer roots
 Weak algebraic highdegree inequalities. Weak highdegree inequalities. Grouping method
 Weak algebraic highdegree inequalities. Weak highdegree inequalities. Perfect square
 Weak algebraic highdegree inequalities. Weak inequalities. Formula of difference of squares
 Weak algebraic highdegree inequalities. Weak inequalities. Factorization of quadratic trinomial
 Weak algebraic highdegree inequalities. Weak inequalities. Properties of fractions
 Weak algebraic highdegree inequalities. Weak inequalities. Difference and sum of cubes

Strict fractional inequalities

 Strict fractional inequalities. Elementary fractional strict algebraic inequalities
 Strict fractional inequalities. Strict fractional algebraic inequalities reduced to strict linear inequalities
 Strict fractional inequalities. Strict fractional algebraic inequalities reduced to strict quadratic inequalities
 Strict fractional inequalities. Strict fractional algebraic inequalities reduced to strict quadratic inequalities. Method of substitution

Weak fractional inequalities

 Weak fractional inequalities. Elementary fractional weak algebraic inequalities
 Weak fractional inequalities. Fractional weak algebraic inequalities reduced to linear inequalities
 Weak fractional inequalities. Fractional weak algebraic inequalities reduced to quadratic inequalities
 Weak fractional inequalities. Fractional weak algebraic inequalities reduced to quadratic inequalities. Method of substitution

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