To solve the inequality [tex]\(2x + 6 > 20\)[/tex], follow these detailed steps:
1. Isolate the term involving [tex]\(x\)[/tex]:
[tex]\[
2x + 6 > 20
\][/tex]
Subtract 6 from both sides to isolate the term involving [tex]\(x\)[/tex]:
[tex]\[
2x + 6 - 6 > 20 - 6
\][/tex]
Simplify the inequality:
[tex]\[
2x > 14
\][/tex]
2. Solve for [tex]\(x\)[/tex]:
Divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[
\frac{2x}{2} > \frac{14}{2}
\][/tex]
Simplify:
[tex]\[
x > 7
\][/tex]
Therefore, the solution to the inequality [tex]\(2x + 6 > 20\)[/tex] is [tex]\(x > 7\)[/tex].
So, the correct choice is:
C. [tex]\(x > 7\)[/tex]
