To solve the equation \(3(x - 4) = 18\) correctly, you can use the method stated in your first option (divide by 3, then add 4).
Let's evaluate the alternatives one by one:
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First, multiply by 13, then subtract 4.
This would not work because the operations apply in a way that doesn't lead to isolating \(x\) correctly. -
First, multiply by \( \frac{1}{3} \), then subtract 4.
This also does not isolate \(x\) correctly, as multiplying by \( \frac{1}{3} \) would not correctly follow the order of operations needed to solve the equation. -
First, distribute the 3, then add 4, and lastly divide by 3.
Distributing the 3 gives \(3x - 12 = 18\). After distributing, we would need to add 12, not 4, to maintain equality, so this option is incorrect. -
First, distribute the 3, then add 12, and lastly divide by 3.
This is correct. Distributing gives \(3x - 12 = 18\), adding 12 results in \(3x = 30\), and dividing by 3 gives \(x = 10\). -
First, divide by 3, then subtract 4.
This method was already mentioned and is correct because after dividing \(3(x - 4) = 18\) by 3, you get \(x - 4 = 6\), and adding 4 yields \(x = 10\).
Thus, the correct alternative method is:
First, distribute the 3, then add 12, and lastly divide by 3.