Learning techniques online - Training problem solving skills - algebraic inequalities

This page was created by EMMentor_Algebra_Inequalities

These pages allow you to try 15 learning techniques out of 57 techniques available in the program EMMentor. Each learning technique applies to the solution of math problem. Select a technique and do what is required at each solution step. If doubt, click an arrow and get this step done. An icon of magnifier allows seeing all steps done. All examples include an option of translation to German (a globe icon). The program EMMentor offers all shown learning techniques. The first two learning techniques are available in the programs EMSolution and EMMentor. At the bottom of this page we offer you to see examples of performance/error analysis available in the program EMMentor.

Learning techniques

Selecting a rule for the next step

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Description

For the current step of solution, the program provides complete info and asks to select a rule that will ground the next solution step. This algorithm trains an understanding of cause-and-effect relationships and active reasoning skills.

Rational inequalities

Weak algebraic high-power inequalities

Weak inequalities. Properties of fractions

Solve the inequality

\frac{v^{3} + 3 v^{2} - 4}{v^{2} + 4 v + 4} \cdot (v - 1) + {(v - 7)}^{2} \geq 7 v^{2} + 2 v + 2 + 2 \cdot (v - 1) \cdot (v - 7)

1. Let's find the domain of definition D(f) for the considered expression, taking into account that the division by zero is not defined

v^{2} + 4 v + 4 \neq 0

Methodical task: Scheme "To select for transformation 2"

To select the formulation for the next step of transformation

Select the continuation

	The theorem "Factorization of quadratic trinomial" reads: If the roots of quadratic trinomial equal to "p" and "q", then this trinomial may be represented as "a(x-p)(x-q)", where "a" is the coefficient at the quadratic term
	Monomials are called the like terms of a polynomial if they differ by the value of a numerical constant only
	A quadratic trinomial is referred to as a polynomial with the highest degree of the unknown equal to two

Hint

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