1. Unit 4.6
Solve Absolute Value Inequalities
Before you solved absolute
equations.
Now you will solve absolute value
inequalities.

2. Example: Using a Number Line
Recall that |x| = 3 means that the
distance between x and 0 is 3.
3
–3
–6 –5 –4 –3 –2 –1 0 1 2 3 4 5
The solutions to the inequality
equation |x| = 3 are 3 and –3.

3. Example: Absolute Value Inequalities
The inequality |x| < 3 means that the
distance between x and 0 is less than 3.
Let’s use the word between to describe
the value inequalities.
-3 < x < 3
–6 –5 –4 –3 –2 –1 0 1 2 3 4 5
Graph of |x| < 3

4. Example: Absolute Value Inequalities
The inequality |x| > 3 means that the
distance between x and 0 is greater than 3.
Let’s use the word beyond to describe the
value inequalities.
x < -3 or x > 3
–6 –5 –4 –3 –2 –1 0 1 2 3 4 5
Graph of |x| > 3

5. Example:
Solve the Inequality |x| ≥ 6 and graph your
solution.
The distance between x and 0 is greater
than or equal 6. So, x ≤ -6 or x ≥ 6.
Let’s use the word beyond to describe the
value inequalities.
–9 –6 –3 0 3 6
Graph of |x| ≥ 6

6. Example:
Solve the Inequality |x| ≤ 0.5 and graph
your solution.
The distance between x and 0 is less than
or equal to 0.5. So, -0.5 ≤ x ≤ 0.5.
Let’s use the word between to describe
the value inequalities.
–1 –0.5 0 0.5
Graph of |x| ≤ 0.5

7. Practice:
Solve the Inequality. Graph the Solution.
1. |x| ≤ 8 Groups 1, 2, 3
2. |u| < 3.5 Groups 4, 5
3. |v| > ⅛ Groups 6, 7

8. Practice:
Solve the Inequality. Graph the Solution.
1. |x| ≤ 8 Groups 1, 2, 3
2. |u| < 3.5 Groups 4, 5, 6
3. |v| > ⅛ Groups 7, 8, 9

9. Start on your homework for tonight:
Textbook Page 229, # 3 - 8