To determine which equation could be solved by multiplying both sides by 4, we can look at each option:
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\(6 + 4x = 1\): If you multiply both sides by 4, the left side becomes \(4(6 + 4x) = 24 + 16x\) and the right side becomes \(4(1) = 4\). Thus, \(24 + 16x = 4\); this is valid.
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\(4 + \frac{x}{6} = 1\): If you multiply both sides by 4, the left side becomes \(4(4 + \frac{x}{6}) = 16 + \frac{4x}{6}\) and the right side becomes \(4(1) = 4\). This does not create a simple equation that can be reduced to a form where multiplying by 4 is useful.
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\(4 + 6x = 1\): If you multiply both sides by 4, the left side becomes \(4(4 + 6x) = 16 + 24x\) and the right side becomes \(4(1) = 4\). This is valid.
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\(6 + \frac{x}{4} = 1\): If you multiply both sides by 4, the left side becomes \(4(6 + \frac{x}{4}) = 24 + x\) and the right side becomes \(4(1) = 4\). This is valid.
From these evaluations, the equations that can be simplified by multiplying both sides by 4 are:
- \(6 + 4x = 1\) (valid)
- \(4 + 6x = 1\) (valid)
- \(6 + \frac{x}{4} = 1\) (valid)
However, the first option \(6 + 4x = 1\) directly leads to the term \(4x\), which is a straightforward multiplication process. The option \(4 + \frac{x}{6} = 1\) is less suitable as dividing or manipulating fractions would not benefit.
Thus, the equation that fits best with the provided feedback is: \(6 + 4x = 1\).