Answer
$x\lt-\frac{7}{2}$ or $x\gt\frac{3}{2}$
Work Step by Step
We simplify as follows:
$3-|x+1|\lt\frac{1}{2}$
$-|x+1|\lt-\frac{5}{2}$
$|x+1|\gt\frac{5}{2}$
$x+1\gt\frac{5}{2}$ or $x+1\lt-\frac{5}{2}$
$x\gt\frac{3}{2}$ or $x\lt-\frac{7}{2}$
