Question

Prove
|x| ≥ x

Answer 1

bcoz if x>=0 then x>=x
and if x<0 then |x|>x
hence |x|>x for all x in R

Answer 2

\[|x| \ge x\]\[(x)^{2} \ge x\]\[x ^{2}-x \ge 0\]\[x (x-1) \ge 0\]\[x \ge 0\]\[x = 1\]