Solve the inequality and graph the solution.

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.