 # Solve an absolute value equation EXAMPLE 2 SOLUTION Rewrite the absolute value equation as two equations. Then solve each equation separately. x – 3 =

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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

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 ? ? Write original inequality. 8 = 8 8 = 8

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

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.

Solve the equation. GUIDED PRACTICE for Examples 2 and 3 r – 7 = 9 2. 16, –2 ANSWER

Solve the equation. GUIDED PRACTICE for Examples 2 and 3 2 s + 4.1 = 18.9 3. 7.4, –7.4 ANSWER

4 t + 9 – 5 = 19 4. GUIDED PRACTICE for Examples 2 and 3 Solve the equation. –3, –15 ANSWER

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