Inequalities with more than one absolute value I saw a question which asked to find all the solutions to:
$|x+2|+|x-5|=7$
For $x\leq -2$, the answer is $-2$. 
For $-2< x <5$, the answer is $R$.
For $x>5$, the answer is $5$.
First I thought the answer should be $(-2, 5)$, but then I realized $-2$ and $5$ solve it too! What would you do?

We have
$$|x+2|+|x-5| = \begin{cases}
-(x+2) - (x-5) & \text{ if } x \leq -2 \\
+(x+2) - (x-5) & \text{ if } 2 < x \leq 5 \\
+(x+2) + (x-5) & \text{ if } x > 5
\end{cases}
$$
Simplifying,
$$|x+2|+|x-5| = \begin{cases}
-2x+3 & \text{ if } x \leq -2 \\
7 & \text{ if } 2 < x \leq 5 \\
2x-3 & \text{ if } x > 5
\end{cases}
$$
So what does this tell us?
