Let's solve the equation step by step.
We have the equation:
[tex]\[
\frac{1}{3} x - \frac{2}{3} = -18
\][/tex]
The first step is to eliminate the fractions to make the equation easier to handle. To do this, we can multiply every term in the equation by 3:
[tex]\[
3 \left( \frac{1}{3} x \right) - 3 \left( \frac{2}{3} \right) = 3(-18)
\][/tex]
Simplifying each term:
[tex]\[
x - 2 = -54
\][/tex]
Next, we need to isolate [tex]\( x \)[/tex]. To do this, add 2 to both sides of the equation:
[tex]\[
x - 2 + 2 = -54 + 2
\][/tex]
This simplifies to:
[tex]\[
x = -52
\][/tex]
Thus, the value of [tex]\( x \)[/tex] in the equation [tex]\(\frac{1}{3} x - \frac{2}{3} = -18\)[/tex] is:
[tex]\[
-52
\][/tex]
So, the correct answer from the given options is:
[tex]\[
-52
\][/tex]
