Answer
$x=.75$ and $x=5$
Work Step by Step
We are given that $|3x+2|=|5x-8|$.
Therefore, $3x+2=5x-8$ and $3x+2=-(5x-8)$.
We can solve both equations to find solutions.
To solve $3x+2=5x-8$ for x, add 8 to both sides.
$3x+10=5x$
Subtract 3x from both sides.
$10=2x$
Divide both sides by 2.
$x=5$
To solve $3x+2=-(5x-8)$, use the distributive property to simplify the right side.
$3x+2=-5x+8$
Subtract 8 from both sides.
$3x-6=-5x$
Subtract 3x from both sides.
$-6=-8x$
Divide both sides by -8.
$x=\frac{6}{8}=.75$