Question

One method for solving 3(x−4)=18
 is to first divide by 3, then add 4. Which method below would also result in the correct answer?(1 point)
Responses

First, multiply by 13
, then subtract 4.
First, multiply by Start Fraction 1 over 3 End Fraction , then subtract 4.

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

First, divide by 3, then subtract 4.
First, divide by 3, then subtract 4.

First, distribute the 3, then add 12, and lastly divide by 3.
First, distribute the 3, then add 12, and lastly divide by 3.
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Answer 1

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.