To solve the inequality \( p - 7 > 1 \), follow these steps:
- Add 7 to both sides of the inequality:
\[ p - 7 + 7 > 1 + 7 \]
This simplifies to:
\[ p > 8 \]
So the solution to the inequality is \( p > 8 \).
Now let's analyze the answer choices:
A. \( p < -6 \)
B. \( p > -6 \)
C. \( p > 8 \) <-- This is the correct choice.
D. \( p < 8 \)
The correct answer is C. \( p > 8 \).
Graphing the solution:
To graph \( p > 8 \):
- Draw a number line.
- Place an open circle at 8 to indicate that 8 is not included in the solution (since the inequality is strict, ">").
- Shade the area to the right of 8 to show all values greater than 8.
Checking the solution:
To check the solution, you can pick a test point greater than 8, such as \( p = 9 \):
\[ 9 - 7 > 1 \implies 2 > 1 \quad \text{(True)} \]
Also, test a point less than 8, say \( p = 7 \):
\[ 7 - 7 > 1 \implies 0 > 1 \quad \text{(False)} \]
Thus, the solution is verified, and we conclude that the solution to the inequality \( p - 7 > 1 \) is indeed \( p > 8 \).