To solve the equation [tex]\(\frac{x}{3} - 14 = -2\)[/tex], follow these steps:
1. Isolate the term with [tex]\(x\)[/tex] on one side of the equation:
[tex]\[
\frac{x}{3} - 14 = -2
\][/tex]
Add 14 to both sides of the equation to eliminate the constant term on the left side:
[tex]\[
\frac{x}{3} - 14 + 14 = -2 + 14
\][/tex]
Simplifying this, we get:
[tex]\[
\frac{x}{3} = 12
\][/tex]
2. Solve for [tex]\(x\)[/tex]:
Now, to solve for [tex]\(x\)[/tex], multiply both sides of the equation by 3 to clear the fraction:
[tex]\[
3 \cdot \frac{x}{3} = 3 \cdot 12
\][/tex]
Simplifying this, we get:
[tex]\[
x = 36
\][/tex]
Therefore, the solution to the equation [tex]\(\frac{x}{3} - 14 = -2\)[/tex] is [tex]\[ \boxed{36} \][/tex] which corresponds to option C.
