Question

Solve the inequality. Graph and check your solutions.
yminus9greater thanminus11
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Part 1
ygreater than
  
enter your response here ​(Simplify your​ answer.)

Answer 1

To solve the inequality \( y - 9 > -11 \), follow these steps:

1. **Add 9 to both sides**:

\[
y - 9 + 9 > -11 + 9
\]

2. **Simplify**:

\[
y > -2
\]

So, the solution to the inequality is:

\[
y > -2
\]

### Graphing the Solution

To graph \( y > -2 \):

1. Draw a number line.
2. Mark the point at \(-2\).
3. Since this is a strict inequality (indicated by the greater than sign, not greater than or equal), draw an open circle at \(-2\).
4. Shade the region to the right of \(-2\) to indicate that \(y\) can take any value larger than \(-2\).

### Checking Solutions

To check if the solution is correct, you can test a number greater than \(-2\) and a number less than or equal to \(-2\).

- **Test \(y = 0\)** (which is greater than \(-2\)):
\[
0 - 9 > -11 \quad \Rightarrow \quad -9 > -11 \quad \text{(True)}
\]

- **Test \(y = -2\)** (which is equal to \(-2\)):
\[
-2 - 9 > -11 \quad \Rightarrow \quad -11 > -11 \quad \text{(False, since this is not greater than)}
\]

- **Test \(y = -3\)** (which is less than \(-2\)):
\[
-3 - 9 > -11 \quad \Rightarrow \quad -12 > -11 \quad \text{(False)}
\]

These checks confirm the solution \(y > -2\) is correct.

### Final Answer

\[
y > -2
\]