1. 1.7 Solving Absolute Value
Equations

2. Solving an Absolute Value Equation
• Absolute value equations can have two
solutions.
• For example, |x| = 5 could have
solutions x = 5 or x = -5
• To solve |ax + b| = c, write as two
equations: ax + b = c or ax + b = -c,
then solve both.

3. Example:
• Solve |2x – 5| = 9

4. Example:
• Solve |x – 3| = -4

5. Your Turn!
• Solve |6x – 3| = 15

6. Solving Inequalities: |ax + b|  c
• |ax + b|  c means ax + b is between –c
and c
• Rewrite as an “and” compound inequality,
then solve.
-c < ax + b < c

7. Example:
• Solve |2x + 7| < 11 and graph the
solution on a number line.

8. Your Turn!
• Solve |-x + 5|  6 and graph the
solution.

9. Solving Inequalities: |ax + b| > c
• |ax + b| > c means ax + b is beyond
–c and c
• Rewrite as an “or” compound
inequality, then solve.
ax + b < -c or ax + b > c

10. Example:
• Solve |3x – 2|  8 and graph the
solution.

11. Your Turn!
• Solve |x + 5| > 12 and graph the
solution.