Question

Solve the inequality. Graph the solution.

4x+8≥2x+20


(1 point)
Responses

Answer 1

To solve the inequality \(4x + 8 \geq 2x + 20\), we can follow these steps:

1. **Subtract \(2x\) from both sides:**

\[
4x - 2x + 8 \geq 20
\]
This simplifies to:
\[
2x + 8 \geq 20
\]

2. **Subtract \(8\) from both sides:**

\[
2x \geq 20 - 8
\]
This simplifies to:
\[
2x \geq 12
\]

3. **Divide both sides by \(2\):**

\[
x \geq \frac{12}{2}
\]
Simplifying gives:
\[
x \geq 6
\]

The solution to the inequality is \(x \geq 6\).

### Graphing the Solution

On a number line, you can represent the solution as follows:

- Draw a number line.
- Shade the region to the right of \(6\).
- Place a closed dot at \(6\) to indicate that \(6\) is included in the solution.

Here is a simple representation:

```
<---|----|----|----|----|----|----|----|----|----|---->
4 5 6 7 8 9 10 11 12 13
●==================>
```

This graph indicates that all values \(x\) greater than or equal to \(6\) are part of the solution to the inequality \(4x + 8 \geq 2x + 20\).