## Precalculus (6th Edition)

The solution is $x=2$
$|3-2x|=|5-2x|$ Solving this absolute value equation is equivalent to solving two separate equations, which are: $3-2x=5-2x$ and $3-2x=-(5-2x)$ $\textbf{Solve the first equation:}$ $3-2x=5-2x$ Take $2x$ to the left side and $3$ to the right side: $-2x+2x=5-3$ $0\ne2$ False This equation has no solution. $\textbf{Solve the second equation:}$ $3-2x=-(5-2x)$ $3-2x=-5+2x$ Take $2x$ to the left side and $3$ to the right side: $-2x-2x=-5-3$ $-4x=-8$ Solve for $x$: $x=\dfrac{-8}{-4}$ $x=2$ The solution is $x=2$