To solve the inequality [tex]\( 3 - \frac{x}{2} \geq 12 \)[/tex], follow these steps:
1. Isolate the variable term:
Start by isolating the term containing [tex]\( x \)[/tex] on one side of the inequality. Subtract 3 from both sides:
[tex]\[
3 - \frac{x}{2} - 3 \geq 12 - 3
\][/tex]
Simplifying, we get:
[tex]\[
-\frac{x}{2} \geq 9
\][/tex]
2. Eliminate the fraction:
To eliminate the fraction, multiply both sides of the inequality by -2. Remember, when you multiply or divide both sides of an inequality by a negative number, the direction of the inequality changes:
[tex]\[
-2 \cdot \left(-\frac{x}{2}\right) \leq -2 \cdot 9
\][/tex]
Simplifying, 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]
Thus, the correct answer is:
B. [tex]\( x \leq -18 \)[/tex]
