Contents

Introduction

Properties

Linear Inequalities 

1  2

Quadratic Inequalities 

Cubic Inequalities

Fractional Inequalities

Modulus Inequalities

Problem Solving

Quiz 

Algebra Main Page

Solving Linear Inequalities

Inequalities are solved in almost the same way as equations.

Example 1

Solve the inequality 2x - 1 > 5

      2x - 1>5

2x -1 + 1 > 5 + 1  (add 1 to both sides)

          2x > 6

            x > 3   (Divide both sides by 2)

Example 2

Solve the inequality 2x - 3 > 2(1 - x) and show it on a number line.

          2x - 3 > 2(1 - x)

             2x - 3 > 2 - 2x

2x - 3 + 3 + 2x > 2 - 2x + 3 + 2x   (add 3 + 2x to both sides) 

                  4x > 5

                    x > 5/4 

Note: The small circle shows that the value 5/4 is not included as a possible answer whereas any number to the right of 5/4 is.

Example 3

Solve the inequality x - 7 5 - 2x and show it on a number line.

x - 7 5 - 2x

x + 2x 5 +7   

      3x 12

        x 4

Note: The circle-dot represents that 4 can be included as a value of x.