Question

Solve the inequality and graph the solution.
4z–6>2

Answer 1

To solve the inequality \(4z - 6 > 2\), follow these steps:

1. **Add 6 to both sides** to isolate the term with \(z\):
\[
4z - 6 + 6 > 2 + 6
\]
This simplifies to:
\[
4z > 8
\]

2. **Divide both sides by 4** to solve for \(z\):
\[
z > \frac{8}{4}
\]
This simplifies to:
\[
z > 2
\]

### Solution
The solution to the inequality is:
\[
z > 2
\]

### Graphing the Solution
To graph this solution on a number line:

- Draw a number line.
- Mark the point \(2\) with an open circle to indicate that \(2\) is not included in the solution (since \(z\) must be greater than \(2\)).
- Shade the region to the right of the point \(2\) to indicate that all numbers greater than \(2\) are included in the solution.

Here's a simple representation of the number line:

```
<---|----|----|----|----|----|----|----|--->
0 1 2 3 4 5 6
(----------------->
```

The open circle at \(2\) signifies that \(2\) is not included in the solution, and the arrow indicates that the solution continues indefinitely to the right.