Appendix A.6

Solving Inequalities

Introduction Solve an inequality

Finding all values of x for which the inequality is true.

The set of all real numbers that are solutions of an inequality is the solution set of the equality

The set of all points on the real number line that represent the solution set is the graph of the inequality.

Properties of Inequalities

Linear Inequalities

The simplest type of inequality is a linear inequality in one variable.

2x + 3 < 4 3x – 3 > x + 7

Example 2 Solving Linear Inequalities

4x2x31.b

9x37x5.a

Solve each inequality

Solution

8x16x297x2

9x37x5.a

The solution set is all real numbers that are greater than 8,which is denoted by (8 , ∞)

2x10x58x52

8x2x32

4x2x31.b

The solution set is all real numbers that are less than or equal to 2,which is denoted by ( -∞ , 2]

Inequalities Involving Absolute Values