Question

Solve the inequality and graph the solution.
1≤j/2–1

Answer 1

To solve the inequality \( 1 \leq \frac{j}{2} - 1 \), we can follow these steps:

1. **Add 1 to both sides**:
\[
1 + 1 \leq \frac{j}{2} - 1 + 1
\]
\[
2 \leq \frac{j}{2}
\]

2. **Multiply both sides by 2** (Note: Since 2 is positive, the inequality does not change direction):
\[
2 \cdot 2 \leq j
\]
\[
4 \leq j
\]
or,
\[
j \geq 4
\]

The solution to the inequality is \( j \geq 4 \).

### Graphing the solution:

On a number line, you can represent this solution:

1. Draw a number line.
2. Place a closed circle (or dot) at 4 to indicate that 4 is included in the solution.
3. Shade the line to the right of 4 to indicate all values greater than 4 are included.

The graph will look like this:

```
<----o=================>
4
```

Where:
- The closed circle at 4 indicates that 4 is part of the solution.
- The shaded arrow to the right indicates all numbers greater than 4 also satisfy the inequality.