To solve the inequality [tex]\(-\frac{1}{2}(d + 6) \geq 9\)[/tex], we will proceed step by step.
1. Isolate [tex]\(d\)[/tex] by getting rid of the fraction:
The inequality is:
[tex]\[
-\frac{1}{2}(d + 6) \geq 9
\][/tex]
2. Eliminate the fraction by multiplying both sides of the inequality by [tex]\(-2\)[/tex]:
Recall that when you multiply or divide both sides of an inequality by a negative number, the direction of the inequality must be reversed. Thus, we multiply both sides by [tex]\(-2\)[/tex]:
[tex]\[
-2 \times -\frac{1}{2}(d + 6) \leq -2 \times 9
\][/tex]
Simplifying both sides gives:
[tex]\[
(d + 6) \leq -18
\][/tex]
3. Solve for [tex]\(d\)[/tex]:
Next, isolate [tex]\(d\)[/tex] by subtracting 6 from both sides:
[tex]\[
d + 6 - 6 \leq -18 - 6
\][/tex]
This simplifies to:
[tex]\[
d \leq -24
\][/tex]
So, the solution to the inequality [tex]\(-\frac{1}{2}(d + 6) \geq 9\)[/tex] is:
[tex]\[
d \leq -24
\][/tex]
Thus, the correct answer is:
[tex]\[
d \leq -24
\][/tex]
