Question

solve the inequality then put it on a numberline
2z–3≥1

Answer 1

To solve the inequality \( 2z - 3 \geq 1 \), follow these steps:

1. Add 3 to both sides:
\[
2z - 3 + 3 \geq 1 + 3
\]
This simplifies to:
\[
2z \geq 4
\]

2. Divide both sides by 2:
\[
\frac{2z}{2} \geq \frac{4}{2}
\]
This simplifies to:
\[
z \geq 2
\]

Now that we have the solution \( z \geq 2 \), we can represent it on a number line.

### Number Line Representation:

- Draw a horizontal line to represent the number line.
- Mark a point for 2 on the line.
- Since the inequality is \( z \geq 2 \), we use a closed circle (●) on 2 to indicate that it is included in the solution.
- Shade the region to the right of 2 to represent all values greater than or equal to 2.

Here is a textual representation:

```
<---|---|---|---|---|---|---|---|---|---|--->
0 1 2 3 4 5 6 7 8 9
●================>
```

The closed circle at 2 indicates \( z = 2 \) is included, and the shading extends infinitely to the right, indicating all numbers greater than 2 are part of the solution.