To solve the equation \( 18x = 6(x - 1) \), we'll first distribute the right side:
\[ 18x = 6x - 6. \]
Next, we'll isolate \( x \) by subtracting \( 6x \) from both sides:
\[ 18x - 6x = -6, \]
which simplifies to:
\[ 12x = -6. \]
Now, divide both sides by \( 12 \):
\[ x = -\frac{6}{12} = -\frac{1}{2}. \]
So, the solution to the equation is:
\[ x = -\frac{1}{2}. \]
Now, to find \( \frac{18x}{6} \):
\[ \frac{18x}{6} = 3x. \]
Substituting \( x = -\frac{1}{2} \) into \( 3x \):
\[ 3x = 3 \left(-\frac{1}{2}\right) = -\frac{3}{2}. \]
Thus, the answer is:
\[ -\frac{3}{2}. \]
To recap:
- The solution to the equation is \( x = -\frac{1}{2} \).
- \( \frac{18x}{6} = -\frac{3}{2} \).