October 26, 2012Compound Inequalities

DO NOW: Review for Quiz!

1. x + 31 > -5

2. -3x ≥ 18

3. 5x – 4 < -34 + 3x

4. 8 more than a number is at least 22.

HW 6.4 WS both sides - all

Lesson 6.4 Compound InequalitiesA Compound Inequality is an inequality

that combines two inequalities in one.Compound Inequalities using “OR”

b > 2 or b ≤ -3“b is greater than 2 or b is less than or

equal to -3”Graph:

10-8 -4 0 4 8-10 -6 2 10-2-10 6

Solving “Or” Inequalities

Example 1: Solve and Graph.

a + 2 < -4 or 2a > -8

10-8 -4 0 4 8-10 -6 2 10-2-10 6

Your turn…

Solve and Graph

1. 3x – 5 ≤ -2 or -5x < -15

2. 3 < 3w or w + 6 ≤ -1

Example 3: Compound Inequalities using “and”

“AND” inequalities are an intersection of the graphs of two inequalities.

Graph: x < 2 and x ≥ -1

10-8 -4 0 4 8-10 -6 2 10-2-10 6

Solving “AND” Inequalities

Example 2: Solve and Graph

6x ≥ -18 and x + 13 < 15

10-8 -4 0 4 8-10 -6 2 10-2-10 6

Example 3 Solve and graph:

- 9 ≤ 4y – 3 ≤ 13

The fancy “and” inequalities

Step 1: Solve as two separate inequalities

Step 2: Graph both inequalities on one graph.

10-8 -4 0 4 8-10 -6 2 10-2-10 6

Guess what??? Your turn…

1. -1 < x + 2 ≤ 8

2. -6x > -36 and x + 23 >25