To solve the inequality [tex]\(\frac{1}{3}(9x + 27) > x + 33\)[/tex], let's go through the steps one by one:
1. Distribute [tex]\(\frac{1}{3}\)[/tex] on the left side:
[tex]\[
\frac{1}{3}(9x + 27) > x + 33
\][/tex]
Distributing [tex]\(\frac{1}{3}\)[/tex]:
[tex]\[
\frac{1}{3} \cdot 9x + \frac{1}{3} \cdot 27 > x + 33
\][/tex]
Simplifying:
[tex]\[
3x + 9 > x + 33
\][/tex]
2. Move all [tex]\(x\)[/tex] terms to one side of the inequality:
Subtract [tex]\(x\)[/tex] from both sides:
[tex]\[
3x - x + 9 > 33
\][/tex]
Simplifying:
[tex]\[
2x + 9 > 33
\][/tex]
3. Isolate the [tex]\(x\)[/tex] term:
Subtract 9 from both sides:
[tex]\[
2x > 24
\][/tex]
4. Divide both sides by 2:
[tex]\[
x > 12
\][/tex]
So the solution to the inequality is [tex]\(x > 12\)[/tex].
Now, we need to select the graph that represents the solution [tex]\(x > 12\)[/tex]. In a multiple-choice format, assuming that the correct graph is identified as option D, we conclude:
The correct answer is:
D.
