To solve the equation \(3(x - 4) = 18\), one effective method is to first divide by 3 and then add 4.
Let's consider the methods listed in your question:
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First, multiply by \( \frac{1}{3} \), then subtract 4.
- Multiplying both sides by \( \frac{1}{3} \) gives \((x - 4) = 6\). Subtracting 4 would not yield the correct solution.
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First, distribute the 3, then add 12, and lastly divide by 3.
- Distributing gives \(3x - 12 = 18\). If you add 12 to both sides, you get \(3x = 30\), and dividing by 3 gives \(x = 10\). This is valid.
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First, distribute the 3, then add 4, and lastly divide by 3.
- Distributing gives \(3x - 12 = 18\). Adding 4 does not lead to a valid operation in solving for \(x\).
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First, divide by 3, then subtract 4.
- Dividing gives \(x - 4 = 6\). Subtracting 4 provides \(x = 10\), which is valid.
From these options, the second method (first distribute the 3, then add 12, and lastly divide by 3) and the fourth method (first divide by 3, then subtract 4) correctly leads to the solution. Thus, the method you are looking for that also results in the correct answer is the second option.