Question

solve the inequality and graph the solution.
2p + 1 ≥ 9
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: Subtract 1 from both sides

$$\begin{align*} 2p+1-1&\geq9 - 1\\ 2p&\geq8 \end{align*}$$

Step2: Divide both sides by 2

$$\begin{align*} \frac{2p}{2}&\geq\frac{8}{2}\\ p&\geq4 \end{align*}$$

To graph \(p\geq4\), we plot a closed endpoint at \(4\) (because the inequality is \(\geq\), which includes equality) and draw an arrow to the right (since \(p\) is greater than or equal to \(4\)).

Answer:

The solution of the inequality \(2p + 1\geq9\) is \(p\geq4\). On the number - line, we have a closed circle at \(4\) and a ray extending to the right.