Answer
$x$ $\geq$ $-4$
The equivalent interval notation is $[-4, \infty)$.
Work Step by Step
$- \frac{2}{3}x - \frac{1}{6}x + \frac{2}{3}(x + 1)$ $\leq$ $\frac{4}{3}$
$- \frac{2}{3}x - \frac{1}{6}x + \frac{2}{3}x + \frac{2}{3}$ $\leq$ $\frac{4}{3}$
$\frac{-4 – 1 + 4}{6}x$ $\leq$ $\frac{4}{3} - \frac{2}{3}$
$\frac{-1}{6}x$ $\leq$ $\frac{2}{3}$
$x$ $\geq$ $- \frac{2 * 6}{3}$ Inequality sign reversed because of multiplication of -6
$x$ $\geq$ $-4$
The equivalent interval notation is $[-4, \infty)$.
