1. 1.4 Absolute Values Solving Absolute Value Equations By putting into one of 3 categories

2. What is the definition of “Absolute Value”? Absolute Value is the distance from 0 on the number line. Mathematically, For example, in, where could x be? 0 -3 3

3. To solve these situations, we will set up 2 “cases” that accurately describe where the inside could be, then solve each. Consider Where could 3x – 2 be? 0 -10 10

4. That was Category 1 Category 1 is used when the absolute value is equal to a number

5. Absolute Value Inequalities Think logically about another situation. What does mean? For instance, in the equation, where on the number line could x  6 be? 0 -5 5 x+6

6. How does that translate into a sentence? Now solve for x. This is Category 2: when x is less than a number

7. Absolute Value Inequalities What does mean? In the equation, where on the number line could 2x  1 be? 0 -11 11 2x+1

8. So, or Now solve for x. This is Category 3: when x is greater than or equal to a number

9. Less than = Leash = Between = And Greater than = Or Note:  is the same as  ;  is the same as  ; just have the sign in the rewritten equation match the original.

10. Examples