Question

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

Answer 1

To solve the inequality \(\frac{x}{3} \geq -1\), you can follow these steps:

1. **Multiply both sides by 3** (since 3 is a positive number, the direction of the inequality will not change):

\[
x \geq -3
\]

Now, you have the solution \(x \geq -3\).

### Part 1: Fill in the response

The response can be completed as follows:

\(x\) **greater than or equals** \(-3\).

### Graphing the solution

To graph the solution \(x \geq -3\):

- Draw a number line.
- From \(-3\), draw a solid or closed circle indicating that \(-3\) is included in the solution (because it is greater than or equal to).
- Shade all values to the right of \(-3\) to indicate that all numbers greater than \(-3\) are included in the solution.

### Checking your solution

To check your solution, you can test a few values:

- **Test value 0** (which is greater than -3):
\[
\frac{0}{3} = 0 \quad \text{and} \quad 0 \geq -1 \quad \text{(true, so the solution is correct)}
\]

- **Test value -4** (which is less than -3):
\[
\frac{-4}{3} = -\frac{4}{3} \quad \text{and} \quad -\frac{4}{3} \geq -1 \quad \text{(false, so it does not satisfy the inequality)}
\]

From these tests, we confirm that the solution \(x \geq -3\) is correct.