#### Answer

$x=\frac{-3b-2c+5}{-b+c}$ or $x=\frac{3b+2c-5}{b-c}$

#### Work Step by Step

We start by distributing. We have $cx+2c-5=bx-3b$. We want the terms with a $x$ to be together, and all the others to be on the other side of the equation. We add $-2c$, $5$, and $-bx$ to both sides of the equation to get $cx-bx=-2c-3b-5$. Now, we factor out $x$ on the left side to get $x(c-b)=-2c-3b+5$. Finally, we divide both sides by $c-b$ to isolate x. This gives us $x=\frac{-2c-3b+5}{c-b}$ but usually we put variables in alphabetical order. $x=\frac{-3b-2c+5}{-b+c}$