Pre-CalculusSection 1.7 Inequalities

Objectives:•To solve linear inequalities.•To solve absolute value inequalities.

Solving an Inequality

To solve an inequality that contains a variable means to find all values of that variable that make the inequality true.

• Unlike an equation, an inequality generally has infinitely many solutions.

• These form an interval or a union of intervals on the number line.

Ex 1. Solve the inequality. Express the solution using interval notation and graph the solution set.

a) 3x < 9x + 4

b) 4 ≤ 3x – 2 < 13

Ex 2. Solve the absolute value inequality. Express the solution using interval notation and graph the solution set.

25 x 1423 xa) b)

Class WorkSolve, graph the solution set, and express the solution set in interval notation.1.5 – 3x ≤ -16

2.-3 ≤ 3x + 7 ≤ ½

3.15x – 4 < 6

4. 4

2

1

x

HW #6 p 84 7-27 eoo, 63-75 eoo, 95, 96