To determine the number by which Rahul can multiply the equation \(y = 23x + 14\) to clear the fractions, we first need to check if there are any fractions in the current equation.
The given equation is:
\[ y = 23x + 14 \]
There are no fractions in this equation. This means that Rahul does not need to multiply by any number to clear fractions.
However, to convert the given equation into standard form, which is typically \(Ax + By = C\), we can rearrange the equation as follows:
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Move \(23x\) to the left side: \[-23x + y = 14\]
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Multiply the entire equation by \(-1\) (though this is not necessary since no fractions exist): \[23x - y = -14\]
In standard form, \(A\) (the coefficient of \(x\)) should be positive, so we can keep it as:
\[ 23x - y = -14 \]
Since there were no fractions in the original equation, the answer to the question is that Rahul does not need to multiply by any number. Therefore, the correct response to the question is:
None of the options provided (12, 3, 6, 4) are correct, as there are no fractions to clear.