Question

Solve the inequality. Graph and check your solution.
pminus6greater than2
Question content area bottom
Part 1
Choose the correct answer below.
A.
pgreater thannegative 4
B.
pless than8
C.
pless thannegative 4
D.
pgreater than8

Answer 1

To solve the inequality \( p - 6 > 2 \), we can isolate \( p \) by following these steps:

1. Add \( 6 \) to both sides:
\[
p - 6 + 6 > 2 + 6
\]
So,
\[
p > 8
\]

The solution to the inequality is \( p > 8 \).

Now, addressing the options given:

A. \( p > -4 \) (Incorrect)

B. \( p < 8 \) (Incorrect)

C. \( p < -4 \) (Incorrect)

D. \( p > 8 \) (Correct)

Thus, the correct answer is **D. \( p > 8 \)**.

To graph this solution:

1. Draw a number line.
2. Plot an open circle at \( 8 \) to indicate that \( 8 \) is not included in the solution.
3. Shade the region to the right of \( 8 \) to represent all values greater than \( 8 \).

To check the solution, you can pick a number greater than \( 8 \), for example, \( 9 \):

Substituting \( 9 \) into the original inequality:
\[
9 - 6 > 2
\]
This simplifies to:
\[
3 > 2
\]
Which is true.

Alternatively, you can pick a number less than or equal to \( 8 \), like \( 8 \) or \( 7 \):
1. For \( 8 \):
\[
8 - 6 > 2
\]
This simplifies to:
\[
2 > 2
\]
This is false.

2. For \( 7 \):
\[
7 - 6 > 2
\]
This simplifies to:
\[
1 > 2
\]
This is also false.

Thus, the solution \( p > 8 \) is confirmed to be correct.