Question

What is the solution of the equation 52x = −18 ?(1 point) Responses 120 Start Fraction 1 over 20 End Fraction −120 negative Start Fraction 1 over 20 Endfraction −516 negative Start Fraction 5 over 16 End Fraction −20

Answer 1

To solve the equation \( 52x = -18 \), we can isolate \( x \) by dividing both sides by 52:

\[
x = \frac{-18}{52}
\]

Next, we simplify the fraction:

\[
x = \frac{-18 \div 2}{52 \div 2} = \frac{-9}{26}
\]

Now, we can convert this to a decimal to see if it matches any of the given responses. The decimal form of \(\frac{-9}{26}\) is approximately -0.346.

None of the provided options explicitly match \(-\frac{9}{26}\) or its decimal approximation.

Therefore, let's check if any of the provided options can be converted or simplified to find a match:
- \(120\)
- \(-\frac{1}{20}\) (which is -0.05)
- \(-120\)
- \(-\frac{5}{16}\) (which is approximately -0.3125)
- \(-20\)

None of these options are equivalent to \(-\frac{9}{26}\).

Therefore, checking the calculations, the solution to \( 52x = -18 \) simplifies to \( x = -\frac{9}{26} \), and does not match any of the given options.