To solve the inequality [tex]\( 2x + 2 > 10 \)[/tex], follow these steps:
1. Subtract 2 from both sides of the inequality to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
2x + 2 - 2 > 10 - 2
\][/tex]
Simplifying this, we have:
[tex]\[
2x > 8
\][/tex]
2. Divide both sides of the inequality by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
\frac{2x}{2} > \frac{8}{2}
\][/tex]
Simplifying this, we get:
[tex]\[
x > 4
\][/tex]
Thus, the correct answer is [tex]\( \boxed{D} \, x > 4 \)[/tex].
