Prove that $|-a|\le a\le |a|$.
Can anyone explain this to me in a step-by-step way?, I am really having trouble in understanding it.
2026-04-08 09:04:49.1775639089
Prove $|-a|\le a\le |a|$
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Assuming you meant $$ -|a|\leq a\leq |a| \, , $$ we will prove this in the following way. The inequality $a\leq|a|$ holds because if $a\geq0$, then we know that $a \leq a$, while if $a<0$, the inequality becomes $a \leq -a$. Since $a$ is negative, this is also true. Hence $$ a\leq|a| \, . $$ A similar approach can be used to prove $-|a| \leq a$.