Prove that $|a|\leq \max\{|b|,|c|\}$ if $b\leq a \leq c$

inequality absolute-value

Prove that $|a| \leq \max\{|b|,|c|\}$ if $b\leq a \leq c$.

I showed that $a\leq c$ and therefore $-c\leq a \leq c$ so that $|a|\leq c$ but then I got stuck.
Is this the right approach?


  • $|a| = a \text{ or } -a$
  • $a \leq c \leq |c|$
  • $- a \leq -b \leq |b|$

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