Question

graph the solution of the inequality.
$2\frac{1}{2} + p > -1\frac{1}{2}$
first select the ray that matches the endpoint (open or closed) and direction (left or right) that you want. then select the location on the number line where you want the endpoint to be located.
-5 -4 -3 -2 -1 0 1 2 3 4 5
←● → ←○ ○→

Explanation:

Step1: Solve the inequality

To solve \(2\frac{1}{2}+p > - 1\frac{1}{2}\), we first subtract \(2\frac{1}{2}\) from both sides.
\(p> - 1\frac{1}{2}-2\frac{1}{2}\)
Convert the mixed numbers to improper fractions: \(-1\frac{1}{2}=-\frac{3}{2}\) and \(2\frac{1}{2}=\frac{5}{2}\)
So \(p>-\frac{3}{2}-\frac{5}{2}=-\frac{8}{2}=-4\)

Step2: Determine the ray properties

Since the inequality is \(p > - 4\) (not \(p\geq - 4\)), the endpoint at \(p = - 4\) is open (because the inequality is strict, no equality). The direction of the ray is to the right (since \(p\) is greater than \(-4\), we shade values to the right of \(-4\) on the number line).

Answer:

The ray should be the open - circle ray pointing to the right (the \( \boldsymbol{\circ
ightarrow} \) symbol) with the endpoint located at \(-4\) on the number line.