Question

Solve the inequality and graph the solution.
–1 > d/2 +1

Answer 1

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.)