Solve.
-$\left| \frac { x + 9 } { 5 } \right| = | 6 x + 8 |$
A) $\left\{ - \frac { 49 } { 31 } , - \frac { 31 } { 29 } \right\}$
B) $\left\{ 1 , \frac { 49 } { 29 } \right\}$
C) $\left\{ - \frac { 17 } { 31 } , \frac { 1 } { 29 } \right\}$
D) $\phi$

Question

Quizplus · Accepted Answer

To solve the equation $\left| \frac { x + 9 } { 5 } \right| = | 6 x + 8 |$, we consider two cases due to the absolute value:1. $\frac { x + 9 } { 5 } = 6 x + 8$2. $\frac { x + 9 } { 5 } = -(6 x + 8)$For the first case, solving for $x$ gives:$$x + 9 = 30x + 40$$$$29x = -31$$$$x = -\frac{31}{29}$$For the second case, solving for $x$ gives:$$x + 9 = -30x - 40$$$$31x = -49$$$$x = -\frac{49}{31}$$Thus, the solution set is $\left\{ - \frac { 49 } { 31 } , - \frac { 31 } { 29 } \right\}$.

Solve - ∣x+95∣=∣6x+8∣\left| \frac { x + 9 } { 5 } \right| = | 6 x + 8 |​5x+9​​=∣6x+8∣

Solve
- $\left| \frac { x + 9 } { 5 } \right| = | 6 x + 8 |$