Answer
The solution set is $\{\frac{-8}{5},7\}$.
Work Step by Step
The given equation is
$\left | 6x+1 \right |=\left | 4x+15 \right |$
Remove absolute value bars.
$ 6x+1 =-( 4x+15 )$ or $ 6x+1 =( 4x+15)$
Clear the parentheses.
$ 6x+1 =-4x-15 $ or $ 6x+1 = 4x+15$
Rearrange.
$ 6x+4x =-15-1 $ or $ 6x-4x =15-1$
Simplify.
$ 10x =-16 $ or $ 2x =14$
$ x =-\frac{16}{10} $ or $ x =7$
$ x =-\frac{8}{5} $ or $ x =7$.
