College Algebra (10th Edition)

$x\lt-\frac{7}{2}$ or $x\gt\frac{3}{2}$
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 $x\lt-\frac{7}{2}$