One method for solving 3(x−4)=18

Let's analyze the equation given:

\[ 3(x - 4) = 18. \]

**Your original method:**
1. Divide both sides by 3:
\[ x - 4 = 6. \]
2. Add 4:
\[ x = 10. \]

Now, let's evaluate the given options to see which one would also yield the correct solution of \( x = 10 \).

1. **First, multiply by 13, then subtract 4.**
- This would not yield the same solution since it alters the equation significantly, producing a different result.

2. **First, multiply by \( \frac{1}{3} \), then subtract 4.**
- This again alters the equation and is not equivalent to the original form. It will not yield \( x = 10 \).

3. **First, distribute the 3, then add 4, and lastly divide by 3.**
- Distributing the 3 gives:
\[ 3x - 12 = 18. \]
Adding 12 to both sides gives:
\[ 3x = 30. \]
Then dividing by 3 results in:
\[ x = 10. \]
- This method works.

4. **First, divide by 3, then subtract 4.**
- This would lead to \( x - 4 = 6 \), and then subtracting 4 wouldn’t yield \( x = 10\).

5. **First, distribute the 3, then add 12, and lastly divide by 3.**
- Distributing gives \( 3x - 12 = 18 \), then adding 12 gives \( 3x = 30 \), then dividing gives \( x = 10 \).
- This method also works.

Now, checking through these methods, we have two correct options which lead to the answer \( x = 10 \):

- **First, distribute the 3, then add 4, and lastly divide by 3.**
- **First, distribute the 3, then add 12, and lastly divide by 3.**

Thus, **both the third and fifth options provide valid methods to solve for \( x \)**. However, it seems you might be looking for only one method. The first validated method is likely the standard solution.

So, the correct answer from the options could be:

**"First, distribute the 3, then add 12, and lastly divide by 3."**

If only one method needs to be selected, that's the appropriate choice among those listed.