1. Solve an absolute value equation EXAMPLE 2 SOLUTION Rewrite the absolute value equation as two equations. Then solve each equation separately. x – 3 = 8 Write original equation. x – 3 = 8 or x – 3 = –8 Rewrite as two equations. x = 11 or x = –5 Add 3 to each side. ANSWER The solutions are 11 and –5. Check your solutions. x – 3 = 8 Solve

2. Solve an absolute value equation EXAMPLE 2 |x – 3| = 8 CHECK Substitute for x. Subtract. Simplify. The solution checks. |11 – 3| = 8 |–5 – 3| = 8 ?? | 8| = 8 |– 8| = 8 ? ? 8 = 8 8 = 8   Write original inequality.

3. Rewrite an absolute value equation EXAMPLE 3 SOLUTION First, rewrite the equation in the form ax + b = c. 3 2x – 7 – 5 = 4 3 2x – 7 = 9 2x – 7 = 3 Write original equation. Add 5 to each side. Divide each side by 3. 3 2x – 7 – 5 = 4. Solve

4. Rewrite an absolute value equation EXAMPLE 3 Next, solve the absolute value equation. 2x – 7 = 3 2x – 7 = 3 or 2x – 7 = –3 2x = 10 or 2x = 4 x = 5 or x = 2 Write absolute value equation. Rewrite as two equations. Add 7 to each side. Divide each side by 2. ANSWER The solutions are 5 and 2.

5. sSolve the equation. GUIDED PRACTICE for Examples 2 and 3 SOLUTION Rewrite the absolute value equation as two equations. Then solve each equation separately. r – 7 = 9 Write original equation. r– 7 = 9 or r – 7 = –9 Rewrite as two equations. r = 16 or r = –2 Add 7 to each side. ANSWER The solutions are 16 and –2. r – 7 = 9 2.

6. Solve the equation. GUIDED PRACTICE for Examples 2 and 3 SOLUTION 2 s + 4.1 = 18.9 Write original equation. Subtract 4.1 from each side. Divide each side by 2. 2 s + 4.1 = 18.9 3. First rewrite the equation in the form ax + b = c 2 s = 14.8 s = 7.4

7. GUIDED PRACTICE for Examples 2 and 3 ANSWER Solue the absolute value equation. s = 7.4 or s = – 7.4 The solution are 7.4 & –7.4

8. SOLUTION First, rewrite the equation in the form ax + b = c. 4 t + 9 – 5 = 19 4 t + 9 = 24 t + 9 = 6 Write original equation. Add 5 to each side. Divide each side by 4. 4 t + 9 – 5 = 19. 4. GUIDED PRACTICE for Examples 2 and 3 Solve the equation.

9. GUIDED PRACTICE for Examples 2 and 3 Solve the absolute value equation. t + 9 = 6 t + 9 = 6 or t + 9 = –6 t = –3 or t = –15 Write absolute value equation. Rewrite as two equations. addition & subtraction to each side