Solve the inequality and graph the solution.

To solve the inequality \( \frac{w}{2} + 43 \geq 41 \), we can follow these steps:

1. Isolate the term with \( w \): Subtract 43 from both sides of the inequality: \[ \frac{w}{2} \geq 41 - 43 \] This simplifies to: \[ \frac{w}{2} \geq -2 \]

2. Eliminate the fraction: Multiply both sides by 2 (note that since we're multiplying by a positive number, the inequality sign does not change): \[ w \geq -4 \]

The solution to the inequality is: \[ w \geq -4 \]

Graphing the solution:

To graph the solution of \( w \geq -4 \):

• Draw a number line.
• Place a solid dot on \(-4\) (indicating that \(-4\) is included in the solution).
• Shade the line to the right of \(-4\), representing all values greater than \(-4\).

Here's a simple representation of the graph:

<----•==========>
     -4

This indicates that \( w \) can take any value greater than or equal to \(-4\).