Question

Solve the inequality. Graph and check your solution.
StartFraction x Over 2 EndFraction greater than minus 3
Question content area bottom
Part 1
x
▼
less than or equals
greater than
less than
greater than or equals
  
enter your response here ​(Simplify your​ answer.)

Answer 1

To solve the inequality \(\frac{x}{2} > -3\), follow these steps:

1. Eliminate the fraction by multiplying both sides of the inequality by 2:
\[
2 \cdot \frac{x}{2} > 2 \cdot -3
\]
This simplifies to:
\[
x > -6
\]

Now, the solution to the inequality is:
\[
x > -6
\]

### Part 1: Complete the Response
You will select "greater than" as the type of inequality and fill in \(-6\):

**x is greater than \(-6\)**.

### Graphing the Solution
To graph the solution:
- Draw a number line.
- Place an open circle over \(-6\) (indicating that \(-6\) is not included in the solution).
- Shade the line to the right of \(-6\) to indicate that all numbers greater than \(-6\) are solutions.

### Checking the Solution
To check if the solution is correct, we can test a number greater than \(-6\) and one less than \(-6\):

1. **Test \(x = 0\) (which is greater than -6)**:
\[
\frac{0}{2} > -3 \implies 0 > -3 \quad \text{(True)}
\]

2. **Test \(x = -7\) (which is less than -6)**:
\[
\frac{-7}{2} > -3 \implies -3.5 > -3 \quad \text{(False)}
\]

Since the first test is true and the second is false, the solution \(x > -6\) is confirmed as correct.