How do I prove that $|c| ≤ \max\{b, −a\}$ given that $a, b, c \in \mathbb R$ and $a ≤ c ≤ b$?

Question

EDIT: I forgot to mention the second condition: $a \leq c \leq b$.

I'm taking a first-year undergraduate calculus course and I'm faced with this problem. I'm not sure about how to proceed without using examples. I realize that $|c|$ might be greater than $b$ or $-a$ depending on the sign of each term.

Answer 1

If $c \geq 0$:

$$|c| \leq b \leq \max(b, -a)$$

If $c < 0$:

$$|c| \leq -a \leq \max(b, -a)$$