Answer
$(-\infty$, $\frac{50}{9})$
Work Step by Step
$\frac{8}{3}(z-4)$$\leq$$\frac{2}{9}(3z+2)$
1. Multiply through
$\frac{8}{3}z$-$\frac{32}{3}$$\leq$$\frac{2}{3}z$+$\frac{4}{9}$
2. Subtract/add from each side to get any polynomials with a variable on one side and any without a variable on the other
$\frac{6}{3}z$$\leq$$\frac{100}{9}$
3. Simplify any possible fractions
2z$\leq$$\frac{100}{9}$
4. Multiply by $\frac{1}{2}$ on both sides to get the variable by itself
z$\leq$$\frac{50}{9}$
5. Plug $\frac{50}{9}$ back into the original problem for z to get $\frac{112}{27}$
6. Test any number between $\frac{112}{27}$ and z$\leq$$\frac{50}{9}$ into the original equation
7. Since any number you test will be negative, your interval starts at $-\infty$ and ends with the interval found earlier: $\frac{50}{9}$
