#### Answer

$z\geq6$

#### Work Step by Step

$2-3z\geq7(8-2z)+12$
Step 1 (Distribute):
$2-3z\geq56-14z+12$
Step 2 (Combine like terms):
$2+11z\geq56+12$ (Added $14z$ to both sides)
$2+11z\geq68$ (Combined $56 + 12$)
$11z\geq66$ (Subtracted $2$ from both sides)
Step 3 (Divide each side by 11);
$11z\geq66$
$z\geq6$
Final step:
When graphing $z\geq6$, be sure to point the arrow from $6$ towards higher values and that the circle is solid since it is $\geq$.