Solve the inequality and graph the solution.

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

1. Add 1 to both sides to isolate the term with \( t \): \[ \frac{t}{2} - 1 + 1 \geq 1 + 1 \] which simplifies to: \[ \frac{t}{2} \geq 2 \]

2. Multiply both sides by 2 to solve for \( t \): \[ 2 \cdot \frac{t}{2} \geq 2 \cdot 2 \] which simplifies to: \[ t \geq 4 \]

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

Graphing the Solution

On a number line, you can represent this solution by shading to the right of 4 to indicate that all numbers greater than or equal to 4 are included in the solution set. A closed circle at 4 denotes that 4 is included in the solution.

Here's a sketch of how you would graph it:

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

• The "o" at 4 is filled in, indicating that 4 is included in the solution.
• The "===" indicates the shading for values greater than 4.