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Solve an absolute value equation

Learn how to solve absolute value equations by rewriting as two separate equations and finding solutions. Practice with guided examples provided.

roberttjohnson
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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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