Answer
x = $-\frac{1}{2}$
Work Step by Step
$\frac{3}{8}x - \frac{1}{6} = -\frac{5}{8}x - \frac{2}{3}$
Add $\frac{5}{8}x$ to both sides:
$\frac{8}{8}x - \frac{1}{6} = -\frac{2}{3}$
x - $\frac{1}{6} = -\frac{2}{3}$
Add $\frac{1}{6}$ to both sides:
x = $-\frac{2}{3} + \frac{1}{6}$
x = $-\frac{4}{6} + \frac{1}{6}$
x = $-\frac{1}{2}$
Check with substitution:
$\frac{3}{8}(-\frac{1}{2}) - \frac{1}{6} = -\frac{5}{8}(-\frac{1}{2}) - \frac{2}{3}$
$-\frac{3}{16} - \frac{1}{6} = \frac{5}{16} - \frac{2}{3}$
$-\frac{1}{6} = \frac{8}{16} - \frac{2}{3}$
$-\frac{1}{6} + \frac{2}{3} = \frac{8}{16} $
$\frac{1}{2} = \frac{1}{2}$
