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: Isolate the term with the variable

Subtract 3 from both sides of the inequality $\frac{z}{2}+3\leq2$.
$\frac{z}{2}+3 - 3\leq2 - 3$
$\frac{z}{2}\leq - 1$

Step2: Solve for z

Multiply both sides of the inequality 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 - 2 (because the inequality includes equality, $\leq$) and draw a ray to the left of - 2.