October 31, 2012Solving Absolute Value Inequalities

DO NOW: Solve.1.

2. │x + 13│ = 8

3. │3x – 9│= -24

2

3x 4

HW 6.5b: Pg. 350 #29-39, skip 36 and 38Unit Test Monday, Nov 5

Lesson 6.5b Solving Absolute Value Inequalities with >, ≥ (greater)

Example 1: Graph the values for x that will satisfy the inequality. Then solve.

│x│≥ 3

5-4 -2 0 2 4-5 -3 1 5-1-5 3

“All values of x whose distance is 3 or more units away from zero.”

Try |x| > 5

Solving Absolute Value Inequalities with <, ≤ (less than)

Example 2: Graph the values for x that will make this true. Then solve.

|x| ≤ 3

5-4 -2 0 2 4-5 -3 1 5-1-5 3

“All values of x whose distance is 3 or less units away from zero.”

Try |x| < 5

Solving Absolute Value Inequalities

Example 3) Solve, then graph

|3x -12| ≥ 6

* Flip the inequality for the negative case.

20-15 -5 5 15-20 -10 10-20 200

Use the same steps you used to solve for Absolute Value Equations!

Set up 2 equations: each for the positive and negative solutions

This these!

1. Solve and graph |2x + 3| < 15

Step 1: Take the inside value and set the two cases, the positive and negative (flip the <)

Step 2: Graph the answer.

Step 3: Write the solution

2. Solve and graph |x – 4| ≥ 10

20-15 -5 5 15-20 -10 10-20 200

Step 1: Take the inside value and set the two cases, the positive and negative (flip the ≥)

Step 2: Graph the answer.

Step 3: Write the solution

The difference between|x| > n and |x| < n

|x| ≥ n (greater than) is n distance or more away from zero and an “OR” compound inequality.

graph OUT

│x│ ≤ n (less than) is within n distance from zero and an “AND” compound inequality.

graph IN

Start practicing on your homework.

HW 6.5b: Pg. 350 #29-39, skip 36 and 38