Question

solve the inequality and graph the solution.
9(z + 3) ≥ -9
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.

Explanation:

Step1: Expand the left side

$$9(z + 3)=9z+27$$
The inequality becomes $9z + 27\geq - 9$.

Step2: Subtract 27 from both sides

$9z+27 - 27\geq - 9-27$.
So, $9z\geq - 36$.

Step3: Divide both sides by 9

$\frac{9z}{9}\geq\frac{-36}{9}$.
We get $z\geq - 4$.

Answer:

The solution of the inequality is $z\geq - 4$. On the number - line, we plot a closed circle at $z = - 4$ (because the inequality is $\geq$, so the endpoint is included) and draw a ray to the right.