1. > Inequalities <≥ ≤
Solving Absolute Value Inequalities
| X |

2. Let’s Review
GRAPH
SIGN
DEFINE / KEY WORD
|X| > OR
|X| <
AND

3. Absolute Value Inequalities
You can think of the absolute value of a real number as the answer to the question …
How far does this real number lie from zero (the origin) on the real number line?

4. Absolute Value Inequalities
Or more simply…
What is the distance between zero and this number?

5. Let’s Continue to Review
|X| > 4 OR
X > 4
X < -4 -4 4

6. Solving Absolute Value Inequalities
and
x – 3 < 5
x – 3 > -5
X < 8
X > -2
-2 < x < 8 -2 8

7. Solving Absolute Value Inequalities
| 8x| > 40 or
8x > 40
8x < -40
8x > 40
8x < -40
X > 5
X < -5 or
-5 > x > 5
-10 -5 5 10

8. Solving Absolute Value Inequalities
| 2x + 1 | > 9 or
2x + 1 > 9
2x + 1 < -9
2x > 8
2x < -10
X > 4
X < -5 or
-5 > x > 4
-10 -5 5 10

9. (show or explain your work in detail…must be legible)
Let’s practice:
Problem
Solve / Graph Problem
(show or explain your work in detail…must be legible)
Answer
(must be legible)
Solve and graph the inequality on a number line.
|c +6| > 12
|n – 5| < 10
|3y| ≥ 27