To solve the inequality [tex]\(3x + 3 - x - 7 > 6\)[/tex] for [tex]\(x\)[/tex], let's break it down step by step.
First, simplify the left-hand side of the inequality:
[tex]\[
3x + 3 - x - 7
\][/tex]
Combine the [tex]\(x\)[/tex] terms together:
[tex]\[
(3x - x) = 2x
\][/tex]
Combine the constant terms together:
[tex]\[
3 - 7 = -4
\][/tex]
So, the inequality simplifies to:
[tex]\[
2x - 4 > 6
\][/tex]
Next, isolate the [tex]\(x\)[/tex] term by adding 4 to both sides of the inequality:
[tex]\[
2x - 4 + 4 > 6 + 4
\][/tex]
This simplifies to:
[tex]\[
2x > 10
\][/tex]
Now, divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[
\frac{2x}{2} > \frac{10}{2}
\][/tex]
Which simplifies to:
[tex]\[
x > 5
\][/tex]
Thus, the solution to the inequality [tex]\(3 x + 3 - x + (-7) > 6\)[/tex] is [tex]\(x > 5\)[/tex].
Therefore, the correct answer is:
D. [tex]\(x > 5\)[/tex]
