Final answer:
All of the provided values, -10, -5, 5, 10, and 15 are solutions to the inequality 118 - 2|p| > 8 since they all fall within the range -55 < p < 55.
Step-by-step explanation:
To find which values of p are solutions to the inequality 118 - 2|p| > 8, we must first isolate the absolute value term.
We start by subtracting 118 from both sides:
-2|p| > 8 - 118
-2|p| > -110
Next, we divide both sides by -2, remembering to reverse the inequality since we're dividing by a negative number:
|p| < 55
This tells us that the values of p must be less than 55 and greater than -55. Checking the options provided:
-10 falls within the range
-5 falls within the range
5 falls within the range
10 falls within the range
15 falls within the range
All of the provided options are solutions to the inequality.