Prove using the triangular inequality that: $|a+b| \geq |a| - |b|$ How can I prove using the triangular inequality that:
$$|a+b| \geq |a| - |b|$$
I already proved it by considering all 8 possible scenarios (like a>b and b=0 ... etc) However I couldn’t manage to find the way to prove it only by using the triangular inequality.

Hint: the inequality you wish to prove is equivalent to
$$|a + b| + |-b| \ge |a|.$$
