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Can we solve the following

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

by taking the intersection of the solutions for

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

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

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

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

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

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