1. Solving and Graphing Absolute Value Inequalities

2. Review of Solving Absolute Value Equations
Example – │x + 2│ = 10 Remember to drop the absolute value sign and set the left side of the equation equal to both 10 and -10. Then solve for x in both equations X + 2 = 10 or x + 2 = -10 So, x = 8 or x = -12

3. How to solve absolute value inequalities
Set up compound inequality using both a positive and negative number
Note: If the inequality is ≥ or >, then use “or” as the conjunction. If the inequality is < or ≤, then use “and” as the conjunction. When the number is negative, change the direction of the inequality.

4. How to solve absolute value inequalities continued
2. Solve the inequalities 3. Graph the inequalities Example – │x + 2│ ≥ 10 x + 2 ≥ 10 or x + 2 ≤ x ≥ 8 or x ≤ -12

5. Graph of the solution x ≥ 8 or x ≤ -12

6. Example of absolute value inequality using “and”
│n – 4│ < 12 Since the inequality is <, then we use “and.” n – 4 < 12 and n – 4 > n < 16 and n > -8

7. Graph the solution n < 16 and n > -8