Question

Solve the inequality. Graph and check your solution.
pminus4less than3
Question content area bottom
Part 1
Choose the correct answer below.
A.
pgreater than7
B.
pgreater thannegative 1
C.
pless thannegative 1
D.
pless than7

Answer 1

To solve the inequality \( p - 4 < 3 \):

1. Add 4 to both sides of the inequality to isolate \( p \):
\[
p - 4 + 4 < 3 + 4
\]
\[
p < 7
\]

So, the solution to the inequality is \( p < 7 \).

Now, looking at the options provided:

A. \( p > 7 \)
B. \( p > -1 \)
C. \( p < -1 \)
D. \( p < 7 \)

The correct answer is:

**D. \( p < 7 \)**

### Graphing the Solution

To graph this solution on a number line:
- Draw a number line.
- Shade to the left of 7 and place an open circle at 7 (since \( p \) is less than, but not equal to, 7).

### Checking the Solution

To check the solution, we can choose a value that is less than 7 (e.g., \( p = 6 \)) and substitute it back into the original inequality:
\[
6 - 4 < 3
\]
\[
2 < 3 \quad \text{(True)}
\]

Now, let's check a value greater than 7 (e.g., \( p = 8 \)):
\[
8 - 4 < 3
\]
\[
4 < 3 \quad \text{(False)}
\]

The checks confirm that the solution \( p < 7 \) is correct.