Question

what kind of number line shows 1/2x-2>0

Answer 1

To solve the inequality \( \frac{1}{2}x - 2 > 0 \) and represent it on a number line, we can follow these steps:

1. **Solve the inequality**:
\[
\frac{1}{2}x - 2 > 0
\]
Add 2 to both sides:
\[
\frac{1}{2}x > 2
\]
Multiply both sides by 2 (note that since 2 is positive, the direction of the inequality does not change):
\[
x > 4
\]

2. **Represent on a number line**:
- Draw a number line.
- Locate the point \( 4 \) on the line.
- Since the inequality is \( x > 4 \), you will represent this with an open circle at \( 4 \) (indicating that \( 4 \) is not included in the solution).
- Shade the line to the right of \( 4 \) (indicating that all values greater than \( 4 \) satisfy the inequality).

Here’s how it would look:

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

The "o" at \( 4 \) indicates that \( 4 \) is not part of the solution, and the shaded area to the right indicates all numbers greater than \( 4 \) are part of the solution to the inequality \( \frac{1}{2}x - 2 > 0 \).