Answer
$-\frac{13}{29},-\frac{15}{13}$.
Work Step by Step
Step 1. Rewrite the equation as $|\frac{8x-1}{3x+2}|=7$, we can remove the absolute sign and separate the cases to: $\frac{8x-1}{3x+2}=7$ and $\frac{8x-1}{3x+2}=-7$
Step 2. For $\frac{8x-1}{3x+2}=7$, we have $8x-1=21x+14\longrightarrow 13x=-15$, thus $x=-\frac{15}{13}$
Step 3. For $\frac{8x-1}{3x+2}=-7$, we have $8x-1=-21x-14\longrightarrow 29x=-13$, thus $x=-\frac{13}{29}$
Step 4. Check the answers and they fit, thus the solutions are $x=-\frac{13}{29}$ and $x=-\frac{15}{13}$.
