Question

solve the inequality and graph the solution.
$$ - 1 < \frac { r } { 2 } + 1 $$
to draw a ray, plot an endpoint and select an arrow. select an endpoint to change it
from closed to open. select the middle of the ray to delete it.

Explanation:

Step1: Solve the inequality

Given \( \frac{-1}{2}\leq r + 1\).
Subtract \(1\) from both sides: \( \frac{-1}{2}-1\leq r\).
Calculate \( \frac{-1}{2}-1=\frac{-1 - 2}{2}=\frac{-3}{2}\). So \(r\geq-\frac{3}{2}\).

Step2: Graph the solution

On the number - line, since \(r\geq-\frac{3}{2}=-1.5\), we plot a closed circle at \(r =-\frac{3}{2}\) (because the inequality is \(\geq\), which includes the endpoint) and draw an arrow to the right (towards larger values of \(r\)).

Answer:

The solution of the inequality is \(r\geq-\frac{3}{2}\). On the number - line, there is a closed circle at \(-1.5\) and an arrow extending to the right.