Proofs of algebraic inequalities

The database of the EMTeachline Mathematics Software contains approximately 5 000 000 of math problems. Math problems are graded in 11 difficulty classes and cover all skill levels from basic through advanced. The software modules are organized by subject. Covered subject areas are Arithmetic, Pre-algebra, Algebra I and II, Trigonometry and Hyperbolic Trigonometry. The Arithmetic and Pre-Algebra modules offer tasks on simplification and evaluation of numeric expressions, including fractional expressions, computational problems, proofs of numeric equalities. The Algebra modules offer simplification and evaluation problems, proofs of algebraic identities and inequalities, solutions of algebraic equations and inequalities; included are linear, quadratic, cubic, reciprocal, biquadratic and fractional expressions. The Trigonometry and Hyperbolic Trigonometry modules offer simplification and evaluation problems, proofs of trigonometric and hyperbolic identities, and solutions of trigonometric and hyperbolic equations; included are all the basic and inverse trigonometric and hyperbolic functions. All problems are solved or proved in full detail. Each module allows employing the database for development of math tests, quizzes, exams, revision exercises and homeworks. Currently available themes, chapters and sections, together with those in preparation, are listed below. Our free online demos allow viewing math examples online.

• 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. Linear expressions and expressions reduced to them.Linear inequalities. Method of substitution. Factorization of quadratic trinomial

• Proof of strict inequalities. Linear expressions and expressions reduced to them.Linear inequalities. Properties of fractions. Distributive law

• Proof of strict inequalities. Linear expressions and expressions reduced to them.Linear inequalities. Properties of fractions. Formulas of short multiplication

• Proof of strict inequalities. Linear expressions and expressions reduced to them.Linear inequalities. Properties of fractions. Properties of powers

• Proof of strict inequalities. Linear expressions and expressions reduced to them.Linear inequalities. Properties of fractions. Factorization of quadratic trinomial

• 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. Formulas of short multiplication

• Proof of strict inequalities. Quadratic expressions.Quadratic inequalities. Distributive law. Rational coefficients

• Proof of strict inequalities. Quadratic expressions.Quadratic inequalities. Factorization of quadratic trinomial

• Proof of strict inequalities. Quadratic expressions.Quadratic inequalities. Properties of powers

• Proof of strict inequalities. Quadratic expressions.Fractional algebraic inequalities

• 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. Quadratic expressions.Fractional inequalities. Method of substitution. Distributive law. Rational coefficients

• Proof of strict inequalities. Quadratic expressions.Fractional inequalities. Method of substitution. Formulas of short multiplication. Integer coefficients

• Proof of strict inequalities. Quadratic expressions.Fractional inequalities. Method of substitution. Formulas of short multiplication. Rational coefficients

• Proof of strict inequalities. Algebraic high-degree expressions.High degrees. Bezout theorem. Standard problems. Integer roots

• Proof of strict inequalities. Algebraic high-degree expressions.High degrees. Bezout theorem. Irrational roots

• Proof of strict inequalities. Algebraic high-degree expressions.High degrees. Bezout theorem. Reducible problems. Integer roots

• Proof of strict inequalities. Algebraic high-degree expressions.High degrees. Bezout theorem. Reducible problems

• Proof of strict inequalities. Algebraic high-degree expressions.High degrees. Grouping method

• Proof of strict inequalities. Algebraic high-degree expressions.High degrees. Perfect square

• Proof of strict inequalities. Algebraic high-degree expressions.High degrees. Bezout theorem. Reducible problems. Irrational roots

• Proof of strict inequalities. Algebraic high-degree expressions.High degrees. Difference of squares

• Proof of strict inequalities. Algebraic high-degree expressions.High degrees. Factorization of quadratic trinomial

• Proof of strict inequalities. Algebraic high-degree expressions.High degrees. Properties of fractions

• Proof of strict inequalities. Algebraic high-degree expressions.High degrees. Difference and sum of cubes

• Proof of strict inequalities. Algebraic high-degree expressions.High degrees. Method of substitution

• Proof of strict inequalities. Fractional algebraic expressions.Elementary fractional algebraic expressions. To prove inequality

• 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

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

• Proof of weak inequalities. Linear expressions and expressions reduced to them.Elementary linear inequalities

• Proof of weak inequalities. Linear expressions and expressions reduced to them.Elementary linear inequalities containing fractions

• Proof of weak inequalities. Linear expressions and expressions reduced to them.Linear inequalities. Distributive law

• Proof of weak inequalities. Linear expressions and expressions reduced to them.Linear inequalities. Formulas of short multiplication

• Proof of weak inequalities. Linear expressions and expressions reduced to them.Linear inequalities. Formulas of short multiplication. Cubes

• Proof of weak inequalities. Linear expressions and expressions reduced to them.Linear inequalities. Properties of powers

• Proof of weak inequalities. Linear expressions and expressions reduced to them.Inequalities reduced to linear inequalities

• Proof of weak inequalities. Linear expressions and expressions reduced to them.Fractional inequalities. Properties of fractions. Rational coefficients

• Proof of weak inequalities. Linear expressions and expressions reduced to them.Fractional inequalities. Properties of fractions. Integer coefficients

• Proof of weak inequalities. Linear expressions and expressions reduced to them.Fractional inequalities. Method of substitution. Integer coefficients

• Proof of weak inequalities. Linear expressions and expressions reduced to them.Fractional inequalities. Method of substitution. Rational coefficients

• Proof of weak inequalities. Linear expressions and expressions reduced to them.Linear inequalities. Factorization of quadratic trinomial

• Proof of weak inequalities. Linear expressions and expressions reduced to them.Linear inequalities. Method of substitution. Distributive law

• Proof of weak inequalities. Linear expressions and expressions reduced to them.Linear inequalities. Method of substitution. Formulas of short multiplication

• Proof of weak inequalities. Linear expressions and expressions reduced to them.Linear inequalities. Method of substitution. Properties of powers

• Proof of weak inequalities. Linear expressions and expressions reduced to them.Linear inequalities. Method of substitution. Factorization of quadratic trinomial

• Proof of weak inequalities. Quadratic expressions.Elementary quadratic inequalities

• Proof of weak inequalities. Quadratic expressions.Quadratic inequalities containing fractions

• Proof of weak inequalities. Quadratic expressions.Quadratic inequalities. Distributive law. Integer coefficients

• Proof of weak inequalities. Quadratic expressions.Quadratic inequalities. Grouping method

• Proof of weak inequalities. Quadratic expressions.Quadratic inequalities. Method of substitution. Distributive law. Integer coefficients

• Proof of weak inequalities. Quadratic expressions.Quadratic inequalities. Method of substitution. Distributive law. Rational coefficients

• Proof of weak inequalities. Quadratic expressions.Quadratic inequalities. Method of substitution. Formulas of short multiplication. Integer coefficients

• Proof of weak inequalities. Quadratic expressions.Quadratic inequalities. Method of substitution. Formulas of short multiplication. Rational coefficients

• Proof of weak inequalities. Quadratic expressions.Quadratic inequalities. Method of substitution. Grouping method

• Proof of weak inequalities. Quadratic expressions.Quadratic inequalities. Method of substitution. Factorization of quadratic trinomial

• Proof of weak inequalities. Quadratic expressions.Fractional inequalities. Method of substitution. Distributive law. Integer coefficients

• Proof of weak inequalities. Quadratic expressions.Fractional inequalities. Method of substitution. Distributive law. Rational coefficients

• Proof of weak inequalities. Quadratic expressions.Fractional inequalities. Method of substitution. Formulas of short multiplication. Integer coefficients

• Proof of weak inequalities. Algebraic high-degree expressions.High degrees. Bezout theorem. Standard problems. Integer roots

• Proof of weak inequalities. Algebraic high-degree expressions.High degrees. Bezout theorem. Reducible problems

• Proof of weak inequalities. Fractional algebraic expressions.Elementary fractional algebraic expressions. To prove inequality

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

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