To solve the inequality [tex]\(3 - \frac{x}{2} \geq 12\)[/tex], follow these steps:
1. Isolate the term involving [tex]\(x\)[/tex]:
Begin by moving the constant term to the other side of the inequality:
[tex]\[
3 - \frac{x}{2} \geq 12
\][/tex]
Subtract 3 from both sides to isolate the term involving [tex]\(x\)[/tex]:
[tex]\[
3 - \frac{x}{2} - 3 \geq 12 - 3
\][/tex]
Simplifying this, we get:
[tex]\[
- \frac{x}{2} \geq 9
\][/tex]
2. Eliminate the fraction:
Since [tex]\(- \frac{x}{2}\)[/tex] means [tex]\(\frac{-x}{2}\)[/tex], multiply both sides of the inequality by -2 to clear the fraction. Remember, when you multiply or divide an inequality by a negative number, the direction of the inequality reverses:
[tex]\[
(-2) \cdot -\frac{x}{2} \leq 9 \cdot (-2)
\][/tex]
Simplifying this, we get:
[tex]\[
x \leq -18
\][/tex]
So the solution to the inequality [tex]\(3 - \frac{x}{2} \geq 12\)[/tex] is [tex]\(x \leq -18\)[/tex].
Therefore, the correct choice is:
B. [tex]\(x \leq -18\)[/tex]
