To solve the equation \( 85x = -10 \), you need to isolate \( x \). You can do this by dividing both sides of the equation by 85:
\[ x = \frac{-10}{85} \]
Now simplify that fraction:
\[ x = \frac{-10 \div 5}{85 \div 5} = \frac{-2}{17} \]
Now, let's see which of the provided options is equivalent to \(-\frac{2}{17}\):
- \( -116 \)
- \( -\frac{1}{16} \)
- \( -58 \)
- \( -\frac{5}{8} \)
- \( -16 \)
- \( -254 \)
None of these options is equal to \(-\frac{2}{17}\). If you were looking for a decimal or further simplification, you could also convert:
\[ -\frac{2}{17} \approx -0.1176 \]
But this does not match any provided options either.
If there was an arrangement or specific condition leading to these choices, please clarify, but based on the arithmetic conducted, the solution \( x = -\frac{2}{17} \) does not correspond to any available responses.