How to solve this absolute value equation and summation question?? $$|2x − 3| − |x + 2| = 5$$

I have no idea. I didn't see anything like this in class. It is a practice question and something like it will come up on the exam can someone please show me the full solution and working (that is how I learn) Thanks in advance.
Hint: using the definition of the absolute value we get $$|2x-3|=\begin{cases} 2x-3, &amp; 2x-3\geq 0 \\ -(2x-3), &amp; 2x-3&lt;0 \end{cases}=\begin{cases} 2x-3, &amp; x\geq \frac{3}{2} \\ -2x+3, &amp; x&lt;\frac {3}{2}\end{cases}$$ 
$$ |x+2|=\begin{cases} x+2, &amp; x+2\geq 0 \\ -(x+2) &amp; x+2&lt;0 \end{cases} = \begin{cases} x+2, &amp; x\geq -2 \\ -x-2, &amp; x&lt;-2\end{cases}$$

This is all we need to simplify the equation. "Something happens" at $x=-2$ and $x=\frac{3}{2}$, one of the terms $|2x-3|$ or $|x+2|$ will change there. Using this we get 3 cases we have to consider:


$x&lt;-2$
$-2\leq x &lt; \frac{3}{2}$
$\frac{3}{2}\leq x$
Hint 

if $x \geq 0$ then you would have $$2x-3 -(x+2) = 5$$

if $x &lt; 0$ then you would have $$-(2x-3) +(x+2) =5$$