Solve for x*x* and graph the solution on the number line below.

2, x, is greater than, minus, 12

2*x*>

−12

Answer




To solve the inequality \(2x > -12\), follow these steps:

### Step 1: Solve the inequality
1. **Divide both sides by 2**:
   \[
   \frac{2x}{2} > \frac{-12}{2}
   \]
2. **Simplify**:
   \[
   x > -6
   \]

So, the solution is \(x > -6\).

### Step 2: Graph the solution on the number line
- On the number line, mark the point \(-6\).
- Since \(x > -6\), you will draw an open circle at \(-6\) (indicating that \(-6\) is not included in the solution).
- Shade the region to the right of \(-6\) to represent all values greater than \(-6\).

Here’s how it would look:

```
<---|---|---|---|---|---|---|---|---|---|---|--->
   -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1
               o----------------------->
```
The open circle at \(-6\) and the arrow to the right indicate that the solution is all numbers greater than \(-6\).

Would you like further details or have any questions?

### Related Questions:
1. How do you solve a similar inequality like \(3x \geq -9\)?
2. What happens if the inequality sign changes from \(>\) to \(<\)?
3. How do you solve and graph the inequality \(4x < 8\)?
4. What is the impact of multiplying or dividing both sides of an inequality by a negative number?
5. How can inequalities be used in real-life situations?

**Tip:** Remember that dividing or multiplying both sides of an inequality by a negative number reverses the inequality sign.

Learn how to solve the inequality 2x > -12 step-by-step and graph the solution on a number line. This problem covers key mathematical concepts including inequalities and graphing techniques. Suitable for students in Grades 7-9.

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