# Math Book 1: Inequalities

An important topic that is very often tested in the GMAT®

I nequalities is an important topic in the GMAT problem solving and GMAT data sufficiency sections. One can expect 2 to 4 questions from this topic. Once the basics are understood and mastered, solving the problem solving variant is quite easy. Watch out for exceptions when solving data sufficiency questions in inequalities in the GMAT.

### Concepts Covered

Wizako's GMAT Math Lesson Book in Inequalities covers the following concepts:

1. Explanation to the basic concept of inequalities.
2. Basic rules governing inequalities such as adding or subtracting a constant to both sides of an inequality.
3. Rules governing multiplying or dividing both sides of an inequality with a negative number.
4. How to solve inequalities that have the unknown in the denominator of an expression?
5. Inequalities in algebraic expressions including linear and quadratic expressions.
6. Inequalities in exponents and comparing two different exponents of an unknown for different range of values along the number line.
7. Inequalities and absolute values (modulus of a number).
8. 18 solved examples, which contain additional notes that help solve questions in inequalities quickly. Includes word problems in inequalities.
9. 17 exercise problems with the answer key and also explanatory answers.
10. A multiple choice test comprising 30 GMAT level questions in inequalities. Explanatory answers and answer key are provided for all questions in the test.

Here is a typical solved example from this chapter.

### Sample Question

Find the range of values of x for which $$frac {1} {x - 2}$ > -2? #### Explanatory Answer There is a linear expression in 'x' in the denominator. Let us eliminate the expression in x in the denominator by multiplying both sides of the inequality by$x - 2)2 in the numerator.

(x - 2)2 is the square of a number and is therefore, always positive for real values of x.
Multiplying both sides of an inequality by a positive number will not affect the sign of the inequality.

(x - 2)2 * $$frac {1} {x - 2}$ >$x - 2)2 * (-2)

(x - 2) > -2(x - 2)2
(x - 2) > -2(x2 - 4x + 4)
(x - 2) > -2x2 + 8x - 8
0 > -2x2 + 7x - 6
Or 2x2 - 7x + 6 > 0

Factorize the expression: 2x2 - 4x - 3x + 6 > 0
(2x - 3) (x - 2) > 0

The range of values of x that satisfy the above inequality are ${$left$ {{$infty },{\frac {3} {2}}} \right$}) $\cup$ $$2,{\infty }$)
In other words, x does not lie between $\frac{3}{2}$ and 2.

### Chapterwise details of Wizako's Math Lesson Books

Math Lesson Book 1

 1 Linear Equations Details 2 Quadratic Equations Details 3 Set Theory Details 4 Sequences & Series Details 5 Number Properties & Theory Details 6 Inequalities Details 7 Functions

Math Lesson Book 2

 1 Descriptive Statistics Details 2 Ratio Proportion Details 3 Mixtures 4 Interest 5 Rates: Speed Distance Details 6 Rates: Races Details 7 Rates: Work Time Details

Math Lesson Book 3

 1 Percents Details 2 Profits Details 3 Permutation Combination Details 4 Probability Details 5 Geometry Details 6 Solid Geometry 7 Coordinate Geometry Details