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Solve an absolute value equation

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

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Solve an absolute value equation

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

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

  3. Solve 32x – 7 – 5 = 4. First, rewrite the equation in the form ax + b = c. 32x – 7 – 5 = 4 32x – 7 = 9 2x – 7 = 3 EXAMPLE 3 Rewrite an absolute value equation SOLUTION Write original equation. Add 5 to each side. Divide each side by 3.

  4. 2x – 7 = 3 ANSWER The solutions are 5 and 2. EXAMPLE 3 Rewrite an absolute value equation Next, solve the absolute value equation. Write absolute value equation. 2x – 7 = 3 or2x – 7 = –3 Rewrite as two equations. 2x = 10 or2x = 4 Add 7 to each side. x = 5 or x = 2 Divide each side by 2.

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

  6. 3. 2 s + 4.1 = 18.9 ANSWER 7.4, –7.4 for Examples 2 and 3 GUIDED PRACTICE Solve the equation.

  7. 4. 4 t + 9 – 5 = 19 ANSWER –3, –15 for Examples 2 and 3 GUIDED PRACTICE Solve the equation.

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