## Intermediate Algebra (6th Edition)

$x=.75$ and $x=5$
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. $x=\frac{6}{8}=.75$