Modulus equations and inequalities

The idea

$|x|$ is the distance from zero, so it is never negative. $|f(x)| = k$ means $f(x) = k$ or $f(x) = -k$. $|f(x)| < k$ means $-k < f(x) < k$.

1. Split into the two cases: positive and negative inside.
2. Solve each case.
3. Check each answer in the original equation: some may not work.

Watch out When the right-hand side contains $x$, check every solution: one may be false.