Contents

Introduction

Properties

Linear Inequalities 

1  2

Quadratic Inequalities 

Cubic Inequalities

Fractional Inequalities

Modulus Inequalities

Problem Solving

Quiz 

Algebra Main Page

Modulus Inequalities

Example 1

Find the solution to the inequality

2x + 5 < 3(|x| + 1)

2x + 5 < 3|x| + 3

2x + 2 < 3|x|

3x < -(2x + 2) or 3x > 2x + 2

5x < -2 or x > 2

The solution is x < -2/5 or x > 2

Example 2

Given that -4 < x < 2 is the solution of |x + a|<b, find the values of a and b.

|x + a|<b

-b < x + a <b

-b - a< x < b - a   = -4 < x < 2

-b - a = - 4 --------(1)

b - a = 2    --------(2)

(1) + (2): -2a = -2

                 a = 1

            b - 1 = 2

                 b = 3

a = 1 and b = 3