Solve the inequality and graph the solution.

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

1. Isolate the term with \(d\): \[ -1 > \frac{d}{2} + 1 \] Subtract \(1\) from both sides: \[ -1 - 1 > \frac{d}{2} \] \[ -2 > \frac{d}{2} \]

2. Eliminate the fraction by multiplying both sides by \(2\): \[ -2 \cdot 2 > d \] \[ -4 > d \] This can be rewritten as: \[ d < -4 \]

The solution to the inequality is: \[ d < -4 \]

Graphing the solution:

To graph this solution on a number line:

1. Draw a number line.
2. Place an open circle at \(-4\) to indicate that \(-4\) is not included in the solution.
3. Shade the line to the left of \(-4\) to show that all values less than \(-4\) are part of the solution.

Number Line Representation:

<---|----|----|----|----|----|----|--->
    -5   -4   -3   -2   -1    0    1
             ( 

(Note: The parentheses indicate that \(-4\) is not included in the solution.)