Adding $2$ absolute values together: $|x+2| + |x-3| =5.$ I came across a very basic absolute value question
$|x+2| + |x-3| =5.$
Initially, I thought the answer was $x=-2$ and $x=3$ because I let each absolute values be either positive and negative and that's what you get.
But the correct answer was an inequality;   $-2\le x \le 3.$ 
Now, If you try subbing values in or solve it graphically, this inequality is correct.
But how am I supposed to know if the solution is to be an inequality or equality? Is there anyway to tell by looking at the expression?
Thanks,

For a more intuitive approach, plotting a graph of $|x+2|$ and $|x-3|$ would help. These are two V-shaped graphs of $\pm45^o $ gradient,  touching the x-axis at $-2$ and $3$ respectively. 
Then you can clearly see that for $-2\leq x\leq3$, the graphs are
$$\begin{align}
&y_1&&=\ \ \ x+2\\
&y_2=-(x-3)&&=-x+3\end{align}$$
giving $y_1+y_2=5$.
Thus the solution to $|x+2|+|x-3|=5$ is $-2\leq x\leq3$. 
