Question

solve the inequality and graph the solution.
15 ≤ 2(z + 14) - 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: Simplify the right - hand side

First, expand and simplify $2(z + 14)-9$.
$2(z + 14)-9=2z+28 - 9=2z + 19$.
So the inequality becomes $15\leq2z + 19$.

Step2: Isolate the variable term

Subtract 19 from both sides of the inequality.
$15-19\leq2z+19 - 19$, which simplifies to $-4\leq2z$.

Step3: Solve for z

Divide both sides of the inequality by 2.
$\frac{-4}{2}\leq\frac{2z}{2}$, so $-2\leq z$.

Answer:

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