# Absolute value with inequalities

Can we solve the following

$|f(x)| + |g(x) | < b$

by taking the intersection of the solutions for

$f(x) + g(x) < b$

$-f(x) - g(x) < b$

$f(x) - g(x) < b$

$-f(x) + g(x) < b$

• A little hint, $a<b$ implies that $-a>-b$ – Zelos Malum Oct 14 '15 at 18:27
• it is too little :( – Ameryr Oct 14 '15 at 18:30
• Yes. It is an equivalence. (And fairly straightforward to show!) – copper.hat Oct 14 '15 at 18:32
• I just want to make sure. Thanks. – Ameryr Oct 14 '15 at 18:49