Question

solve the inequality and graph the solution.
1 < p + 2
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.
submit

Explanation:

Step1: Isolate the variable \( p \)

Subtract \( 2 \) from both sides of the inequality \( 1 < p + 2 \).
Using the subtraction property of inequalities: \( 1-2 < p+2 - 2 \).
Simplify the left - hand side: \( - 1 < p \), which can be rewritten as \( p>-1 \).

Step2: Graph the solution

The inequality \( p > - 1 \) means that \( p \) can take any value greater than \( - 1 \).
On the number line, we use an open circle at \( p=-1 \) (because \( p=-1 \) is not included in the solution set, since the inequality is strict, i.e., \( > \) not \( \geq \)) and draw a ray to the right of \( - 1 \).

Answer:

The solution of the inequality \( 1 < p + 2 \) is \( p>-1 \). On the number line, there is an open circle at \( - 1 \) and a ray extending to the right.