To solve the equation \(52x = -18\), you need to isolate \(x\). You can do this by dividing both sides of the equation by 52:
\[ x = \frac{-18}{52} \]
Now, simplify \(-\frac{18}{52}\). Both 18 and 52 can be divided by 2:
\[ x = \frac{-9}{26} \]
Now, we'll need to check if \(-\frac{9}{26}\) corresponds to any of the provided options:
- \(-\frac{5}{16}\)
- \(-\frac{1}{20}\)
- \(-20\)
- \(\frac{1}{20}\)
None of these options are equivalent to \(-\frac{9}{26}\), which suggests that there may have been an error regarding the options provided or their relation to the equation.
Therefore, the solution to the equation \(52x = -18\) is \(x = -\frac{9}{26}\), which does not match any of the options given.