Solve the absolute value equation. $$| 12 + 2 x | = | x - 6 |$$
A) { }
B) $\{ - 18 , - 2 \}$
C) $\{ - 18 \}$
D) $\{ - 18 , - 6 \}$

Question

Solve the absolute value equation. $$| 12 + 2 x | = | x - 6 |$$
A) {  }
B) $\{ - 18 , - 2 \}$
C) $\{ - 18 \}$
D) $\{ - 18 , - 6 \}$

Quizplus · Accepted Answer

To solve the absolute value equation $| 12 + 2 x | = | x - 6 |$, we consider two cases due to the property of absolute values:1. **Case 1:** $12 + 2x = x - 6$   - Subtract $x$ from both sides: $12 + x = -6$   - Subtract 12 from both sides: $x = -18$2. **Case 2:** $12 + 2x = -(x - 6)$   - This simplifies to $12 + 2x = -x + 6$   - Add $x$ to both sides and subtract 6: $3x = -6$   - Divide by 3: $x = -2$Therefore, the solution set is $\{-18, -2\}$.

Solve the Absolute Value Equation ∣12+2x∣=∣x−6∣| 12 + 2 x | = | x - 6 |∣12+2x∣=∣x−6∣

Solve the Absolute Value Equation $| 12 + 2 x | = | x - 6 |$