## Answer :

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]