To solve the inequality \( 3 - \frac{x}{2} \leq 18 \), we'll follow these steps:
1. Isolate the term involving \( x \):
[tex]\[
3 - \frac{x}{2} \leq 18
\][/tex]
Subtract 3 from both sides to isolate the term containing \( x \):
[tex]\[
3 - \frac{x}{2} - 3 \leq 18 - 3
\][/tex]
Simplifying this gives:
[tex]\[
-\frac{x}{2} \leq 15
\][/tex]
2. Eliminate the fraction:
Multiply both sides of the inequality by \(-2\) to solve for \( x \). It's important to remember that when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign:
[tex]\[
-2 \left( -\frac{x}{2} \right) \geq -2 \times 15
\][/tex]
Simplifying this results in:
[tex]\[
x \geq -30
\][/tex]
So the solution to the inequality \( 3 - \frac{x}{2} \leq 18 \) is \( x \geq -30 \).
Finally, let's match our solution with the answer choices provided:
- A. \( x \leq 42 \)
- B. \( x \leq -30 \)
- C. \( x \geq -30 \)
- D. \( x \geq -42 \)
The correct answer is C. [tex]\( x \geq -30 \)[/tex].
