Question

now its time to practice on your own
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.
(number line from -5 to 5 with tick marks at each integer, and some ray selection icons below)

Explanation:

Step1: Solve the inequality for \( p \)

Subtract \( 2\frac{1}{2} \) from both sides of the inequality \( 2\frac{1}{2}+p > - 1\frac{1}{2} \).
First, convert the mixed numbers to improper fractions: \( 2\frac{1}{2}=\frac{5}{2} \) and \( - 1\frac{1}{2}=-\frac{3}{2} \).
So the inequality becomes \( p>-\frac{3}{2}-\frac{5}{2} \).
Calculate the right - hand side: \( -\frac{3 + 5}{2}=-\frac{8}{2}=-4 \). So \( p > - 4 \).

Step2: Determine the endpoint and direction on the number line

• Endpoint type: Since the inequality is \( p > - 4 \) (not \( p\geq - 4 \)), the endpoint at \( p=-4 \) is an open circle (because the value \( - 4 \) is not included in the solution set).
• Direction: For the inequality \( p > - 4 \), the values of \( p \) that satisfy the inequality are all numbers greater than \( - 4 \). So the ray should point to the right (towards positive infinity) starting from the open circle at \( - 4 \) on the number line.

To graph the solution: Place an open circle at \( - 4 \) on the number line and draw a ray pointing to the right (towards numbers greater than \( - 4 \), like \( - 3,-2,\cdots\)).

Answer:

The solution to the inequality \( 2\frac{1}{2}+p > - 1\frac{1}{2} \) is \( p > - 4 \). To graph it, use an open circle at \( - 4 \) and a ray pointing to the right.