To solve the equation \(3(x - 4) = 18\), one valid method is to first divide by 3, giving you \(x - 4 = 6\), and then add 4 to find \(x = 10\).
Let's evaluate the options given:
A: First, distribute the 3, then add 12, and lastly divide by 3.
- Distributing the 3 gives you \(3x - 12 = 18\). Adding 12 gives you \(3x = 30\), and then dividing by 3 gives \(x = 10\). This method works.
B: First, multiply by 13, then subtract 4.
- This doesn't follow a valid algebraic method for this problem.
C: First, multiply by \(\frac{1}{3}\), then subtract 4.
- Multiplying by \(\frac{1}{3}\) gives you \(\frac{1}{3} \cdot 3(x - 4) = \frac{1}{3} \cdot 18\), simplifying to \(x - 4 = 6\). Subtracting 4 gives \(x = 2\), which is incorrect.
D: First, distribute the 3, then add 4, and lastly divide by 3.
- Distributing gives \(3x - 12 = 18\). Adding 4 results in \(3x - 8 = 18\). Dividing by 3 does not yield the correct result.
E: First, divide by 3, then subtract 4.
- Dividing gives \(x - 4 = 6\). Subtracting 4 here does not follow the correct sequence.
Out of these options, only A successfully leads to the correct solution:
The correct answer is A.