Solve the equation.
-$$| - 8 + 3 x | = | 7 - 4 x |$$
A) $\left\{ \frac { 15 } { 7 } , - 1 \right\}$
B) $\left\{ \frac { 1 } { 7 } , 1 \right\}$
C) $\left\{ - \frac { 1 } { 7 } , 1 \right\}$
D) $\left\{ - 15 , \frac { 1 } { 7 } \right\}$

Question

Quizplus · Accepted Answer

To solve $| - 8 + 3 x | = | 7 - 4 x |$, we consider two cases due to the absolute value:1. $ - 8 + 3 x = 7 - 4 x $ and 2. $ - 8 + 3 x = - (7 - 4 x) $For case 1, solving $ - 8 + 3 x = 7 - 4 x $ gives $ 7 x = 15 $, so $ x = \frac{15}{7} $.For case 2, solving $ - 8 + 3 x = - 7 + 4 x $ gives $ x = -1 $.Thus, the solution set is $ \left\{ \frac { 15 } { 7 } , - 1 \right\} $.

Solve the Equation ∣−8+3x∣=∣7−4x∣| - 8 + 3 x | = | 7 - 4 x |∣−8+3x∣=∣7−4x∣

Solve the Equation $| - 8 + 3 x | = | 7 - 4 x |$