Question

Use a proof by cases to prove the following:
If -a < x < a, then |x| < a.

Answer 1

|x|<a

which mean either (x)<a or (-x)<a
-x<a ---> x>-a

Answer 2

\[\left| x \right| = \pm x\]

Answer 3

\[x > -a\]
\[x < a\]