1. 2.6 Solving Absolute-Value Inequalities
Objective
Solve absolute-value inequalities.
Essential Question: How do you graph an absolute value inequality?

2. x  1 You must reverse the symbol and the sign
Solving an Absolute-Value Inequality
Solve | x  4 | < 3
You must write two inequalities
You must reverse the symbol and the sign
x  4  3
x – 4 < 3 
Reverse inequality symbol.
x < 7
x  1
The solution is all real numbers greater than 1 and less than 7.
This can be written as 1  x  7.
4 3 2 

3. or | 2x + 1 | > 9 2x + 1 > 9 2x  1  9  – 1 – 1 –1 –1
Solving an Absolute-Value Inequality
Solve | 2x  1 | 3  6
| 2x + 1 | > 9
2x + 1 > 9
2x  1  9 
– 1 – 1
–1 –1
2x  10
2x  8
x  4 or
x  5
Reverse inequality symbol.
 6  5  4  3  2 

4. and Solve | 3x + 1 | < 5 3x + 1 < 5 3x + 1> -5 -1 -1 – 1 – 1
– 1 – 1
3x < 4
3x > –6
x <
and
X > -2

5. What about these?
Determine numbers that are true and untrue.
|x – 2| < -4
|x + 2| > -4
All real numbers are true? Why
No solutions. Why?

6. Try these Solve the equation. 1. 2.
Match the inequality with the graph of its solution. 3. A. or 4. B. or 5. C.
and