To solve the equation \(3(x-4) = 18\), we can explore different methods that will lead to the correct answer.
- The original proposed method involves first dividing by 3, then adding 4: \[ x - 4 = \frac{18}{3} \Rightarrow x - 4 = 6 \Rightarrow x = 6 + 4 \Rightarrow x = 10. \]
Let's analyze the other methods provided:
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First, multiply by 13, then subtract 4.
- This is not a valid operation in this context and would not yield the correct result.
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First, multiply by \( \frac{1}{3} \), then subtract 4.
- This method would first change the equation to \( x - 4 = 6 \), leading to the wrong results, as multiplying the entire equation by \( \frac{1}{3} \) is not appropriate.
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First, distribute the 3, then add 4, and lastly divide by 3.
- Distributing the 3 first yields \( 3x - 12 = 18 \). Adding 4 results in \( 3x - 8 = 18 \), and then dividing by 3 would lead to \( x - \frac{8}{3} = 6 \), which is incorrect.
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First, distribute the 3, then add 4, and last divide by 3.
- This is essentially the same as the previous method phrased differently and would also lead to a wrong direction.
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First, divide by 3, then subtract 4.
- This accurately reflects the original proposed method but does not yield new insights.
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First, distribute the 3, then add 12, and lastly divide by 3.
- Distributing gives \( 3x - 12 = 18 \). Adding 12 results in \( 3x = 30 \), and dividing by 3 gives us \( x = 10 \), which is correct.
Thus, the method that also results in the correct answer is: First, distribute the 3, then add 12, and lastly divide by 3.