Question

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

Answer 1

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

1. **Isolate the term with \( u \)**:
\[
\frac{u}{2} + 1 > -1
\]
Subtract 1 from both sides:
\[
\frac{u}{2} > -1 - 1
\]
Simplifying the right side:
\[
\frac{u}{2} > -2
\]

2. **Eliminate the fraction**:
Multiply both sides by 2 (since 2 is positive, the inequality sign does not change):
\[
u > -4
\]

The solution to the inequality is:
\[
u > -4
\]

### Graphing the solution:

To graph the solution \( u > -4 \):

- Draw a number line.
- Locate -4 on the number line.
- Since the inequality is strict (greater than, not greater than or equal to), draw an open circle at -4 to indicate that -4 is not included in the solution.
- Shade the line to the right of -4 to indicate that all values greater than -4 are included in the solution.

Here’s a representation of the graph:
```
<---|---|---|---|---|---|---|---|---|--->
-5 -4 -3 -2 -1 0 1 2 3
(------------------->
```

In this graph, the parenthesis at -4 indicates that -4 is not included in the solution, and the arrow shows that the solutions extend to positive infinity.