1. Goal: Solve and write absolute value equations in one variable Section 4-4: Solving Absolute Value Equations

2. Warm - Ups Solve the equations: 1. 3x + 15 = -42 2. 5x – 8 = 7 3. 2x + 1 = -3

3. Absolute ValueAbsolute Value Equations written as |x| distance the number is from 0 on a number line is never negative because it is a distance If x is positive : |x| = x If x is zero: |x| = 0 If x is negative: |x| = x Of the form |x| = c where c>0 Can have two possible values for x that make the statement true: a positive value c and a negative value -c

5. Example 1: Solve an Absolute Value Equation Solve |5 – 2x| = 9

6. Example 1: Continued Solve |3 – 4x | = 11

7. Example 2: Solve an Absolute Value Equations Solve | 3x – 9| - 10 = 14

8. Example 2: Solve an Absolute Value Equations Solve |2x – 8| + 7 = 13

9. Checkpoint: Solve the Absolute Value Inequalities and check your solution. |x + 2| = 5 |x – 6| = 7

10. Checkpoint: Solve the Absolute Value Inequalities and check your solution. |3x + 6| + 4 = 4|4x – 3| - 1 = 2

11. Example 3: Write an Absolute Value Equations

12. Checkpoint: Write an Absolute Value Equation Write an absolute value equation that has 3 and 7 as its solutions. Write an absolute value equation that has -4 and 10 as its solutions.