Question

Solve the inequality. Graph and check your solutions.
yplus2greater thannegative 8
Question content area bottom
Part 1
Choose the correct answer below.
A.
yless thannegative 6
B.
ygreater thannegative 6
C.
yless thannegative 10
D.
ygreater thannegative 10

Answer 1

To solve the inequality \( y + 2 > -8 \), you need to isolate \( y \).

1. Subtract 2 from both sides:
\[
y + 2 - 2 > -8 - 2
\]
\[
y > -10
\]

So the correct answer is:
**D. \( y > -10 \)**.

### Graphing the Solution
To graph the solution on a number line:
1. Draw a number line.
2. Place an open circle at -10 (this denotes that -10 is not included in the solution).
3. Shade the region to the right of -10 to indicate that \( y \) can take any value greater than -10.

### Checking Solutions
1. **Check \( y = -9 \)**:
\[
-9 + 2 = -7
\]
\(-7 > -8\) is true, so \( y = -9 \) is a solution.

2. **Check \( y = -10 \)**:
\[
-10 + 2 = -8
\]
\(-8 > -8\) is false, so \( y = -10 \) is not a solution.

3. **Check \( y = -11 \)**:
\[
-11 + 2 = -9
\]
\(-9 > -8\) is true, so \( y = -11 \) is also a solution.

### Conclusion
The solution to the inequality \( y + 2 > -8 \) is \( y > -10 \), and it has been correctly graphed and verified. The chosen answer is indeed **D. \( y > -10 \)**.