To solve the equation \(-35(15x - 30) = 198\), let's follow the steps:
- First, distribute the \(-35\) on the left side of the equation:
\[ -35 \cdot 15x + 35 \cdot 30 = 198 \]
This simplifies to:
\[ -525x + 1050 = 198 \]
- Next, isolate the term with \(x\). Subtract \(1050\) from both sides:
\[ -525x = 198 - 1050 \] \[ -525x = -852 \]
- Divide both sides by \(-525\) to solve for \(x\):
\[ x = \frac{-852}{-525} \] \[ x = \frac{852}{525} \]
- Now simplify this fraction by finding the greatest common divisor (GCD) of \(852\) and \(525\). The GCD is \(3\).
\[ x = \frac{852 \div 3}{525 \div 3} = \frac{284}{175} \]
The value of \(x\) does not match any of the suggested answers exactly, which all appear to be integers.
Let's check if any of the options are reasonable as integer solutions or if an error might have occurred in the simplification process.
- Checking the approximate decimal value: \[ x = \frac{284}{175} \approx 1.63 \]
This does not correspond with any of the provided options (\( -24, -36, -10, -20 \)). Therefore, it seems the problem might have an incorrect set of choices, as the simplification leads to \( \frac{284}{175} \).
If there is a need for a re-evaluation or checking the initial equation, please clarify. However, based on the calculations, none of the provided options (\( x = -24, -36, -10, -20 \)) is correct according to the solution derived from the equation.
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