Chapter 1 - Review Exercises - Page 145: 31

{$x|-\frac{3}{2}\lt\ x\lt-\frac{7}{6}$}

We simplify as follows: $|3x+4|\lt\frac{1}{2}$ $-\frac{1}{2}\lt3x+4\lt\frac{1}{2}$ $-1\lt6x+8\lt1$ $-9\lt6x\lt-7$ $-\frac{3}{2}\lt x\lt-\frac{7}{6}$ {$x|-\frac{3}{2}\lt\ x\lt-\frac{7}{6}$}