Let's analyze each option to see which method would also result in the correct answer for the equation \(3(x - 4) = 18\).
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First, divide by 3, then subtract 4.
- If we divide both sides by 3: \[ x - 4 = 6 \]
- Then subtracting 4 gives: \[ x = 10 \] This method is incorrect, as subtracting 4 from 6 does not give the correct value.
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First, multiply by \(\frac{1}{3}\), then subtract 4.
- Multiplying both sides by \(\frac{1}{3}\): \[ x - 4 = 6 \]
- Then subtracting 4 gives: \[ x = 10 \] This is also equivalent to the first method since multiplying by \(\frac{1}{3}\) is the same as dividing by 3, and it results in the same incorrect method as above.
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First, distribute the 3, then add 4, and lastly divide by 3.
- Distributing gives: \[ 3x - 12 = 18 \]
- Adding 12 gives: \[ 3x = 30 \]
- Dividing by 3 yields: \[ x = 10 \] This leads us to the same incorrect solution.
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First, distribute the 3, then add 12, and lastly divide by 3.
- Distributing gives: \[ 3x - 12 = 18 \]
- Adding 12 gives: \[ 3x = 30 \]
- Dividing by 3 yields: \[ x = 10 \] This again results in the same incorrect solution.
Upon reviewing these methods, none of the four listed methods result in the correct solution of \(x = 10\) for the original equation \(3(x-4)=18\). Thus, it seems that there may be some misunderstanding in the options provided or they might be phrased in a certain way that leads to the same equation manipulation.
However, the following are valid transformations that lead to the correct solution of the equation based on the direct methods (e.g., initial methods of division or addition/subtraction). Among the given methods, mathematically consistent methods would inherit the same logical constructs, yielding similar results.
Thus, based on our re-evaluation, it is apparent that none of the proposed methods provide alternative correct results distinct from one another given they repeat the process yielding identical forms or outcomes.
If you have a specific direction or alternative steps you would like evaluated in consideration of the problem, please clarify so that I can assist accordingly!