Answer
$\left\{ \frac{1}{2},\frac{13}{4} \right \}$.
Work Step by Step
The given equation is
$\Rightarrow \left | x+5\right |=\left | 5x-8\right |$
Rewrite the equation without absolute value bars.
$\Rightarrow x+5=5x-8$ or $x+5=-(5x-8)$
Solve both equations separately.
First equation.
$\Rightarrow x+5=5x-8$
Add $8-x$ to both sides.
$\Rightarrow x+5+8-x=5x-8+8-x$
Add like terms.
$\Rightarrow 13=4x$
Divide both sides by $4$.
$\Rightarrow \frac{13}{4}=\frac{4x}{4}$
Simplify.
$\Rightarrow \frac{13}{4}=x$
Switch the values.
$\Rightarrow x=\frac{13}{4}$
Second equation.
$\Rightarrow x+5=-(5x-8)$
Clear the parentheses.
$\Rightarrow x+5=-5x+8$
Add $5x-5$ to both sides.
$\Rightarrow x+5+5x-5=-5x+8+5x-5$
Simplify.
$\Rightarrow 6x=3$
Divide both sides by $6$.
$\Rightarrow \frac{6x}{6}=\frac{3}{6}$
Simplify.
$\Rightarrow x=\frac{1}{2}$
Hence, the solution set is $\left\{ \frac{1}{2},\frac{13}{4} \right \}$.
