Solve the inequality and graph the solution.

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.