Question

Solve the inequality. Graph and check your solutions.
yplus5less thannegative 7
Question content area bottom
Part 1
Choose the correct answer below.
A.
yless thannegative 2
B.
ygreater thannegative 12
C.
yless thannegative 12
D.
ygreater thannegative 2

Answer 1

To solve the inequality \( y + 5 < -7 \), we first isolate \( y \).

1. Subtract 5 from both sides:

\[
y < -7 - 5
\]

2. Simplifying the right side gives:

\[
y < -12
\]

So the solution to the inequality is \( y < -12 \).

Now, let's check the answer options:

- A. \( y < -2 \) (Incorrect)
- B. \( y > -12 \) (Incorrect)
- C. \( y < -12 \) (Correct)
- D. \( y > -2 \) (Incorrect)

The correct answer is **C. \( y < -12 \)**.

### Graphing the solution:
To graph \( y < -12 \):

- Draw a horizontal line at \( y = -12 \).
- Since it is a strict inequality (<), the line is dashed, indicating that -12 is not included in the solution.
- Shade the region below the line to represent all values less than -12.

### Checking the solution:
Select a test point, such as \( y = -13 \):

Substituting into the original inequality:
- \( -13 + 5 < -7 \)
- \( -8 < -7 \) (True)

This confirms that the solution \( y < -12 \) is correct.

So the final answer is **C. \( y < -12 \)**.