Question

Solve the inequality. Graph and check your solution.
pminus7greater than1
Question content area bottom
Part 1
Choose the correct answer below.
A.
pless thannegative 6
B.
pgreater thannegative 6
C.
pgreater than8
D.
pless than8

Answer 1

To solve the inequality \( p - 7 > 1 \), follow these steps:

1. 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 \( p > 8 \).