Question

solve the inequality and graph the solution.
$\frac{z}{2}+3leq2$
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: Subtract 3 from both sides

$\frac{z}{2}+3 - 3\leq2 - 3$
$\frac{z}{2}\leq - 1$

Step2: Multiply both sides by 2

$2\times\frac{z}{2}\leq2\times(-1)$
$z\leq - 2$

Answer:

The solution of the inequality is $z\leq - 2$. On the number - line, we plot a closed circle at $z = - 2$ (since the inequality is $\leq$) and draw a ray to the left of $-2$.