1. Absolute Value Equations & Inequalities

2. Review: Absolute Value The magnitude of a real number without regard to its sign. OR Distance of value from zero regardless of sign.

3. Two Methods to Solving Absolute Value Method One: – Solve equation like normal – Consider positive and negative solutions at end – Warning!!!: Use when there is only a variable is inside absolute value sign 7 + || = 17

4. Example

5. Two Methods to Solving Absolute Value Method Two: – Remove absolute value signs by setting one equation to a negative and the equation to a positive – Solve like normal – Can use ALL the time. – MUST use when there are multiple terms inside absolute value sign

6. Example

7. Solving Tip # 1

8. Solving Tip # 2

9. Let’s Practice… Choose your method & solve: 1.4|v  5| = 16 2.3|d  4| = 12

10. Let’s Practice…

11. Absolute Value Inequalities Absolute Value Inequalities are a form of Compound Inequalities. How to Solve: – Separate – Solve – Graph both solutions.

12. Example

13. Let’s Practice… Solve and graph each solution. 1.|f – 1| ≤ 6 2. 2|p + 3| ≥ 10