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?

First divide by 3, then subtract 4

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

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

First, multiply by 1.3 then subtract 4

Answer 1

So which one

Answer 2

To solve the equation \( 3(x - 4) = 18 \), we can check which of the proposed methods will also lead to the correct solution.

1. **First divide by 3, then subtract 4:**
- Dividing both sides by 3 gives \( x - 4 = 6 \).
- Then, subtracting 4 gives \( x = 6 + 4 = 10 \).
- This method does not yield the correct answer, as \( x - 4 \) should equal 6 and we need to add 4, not subtract it.

2. **First distribute the 3, then add 4, and lastly divide by 3:**
- Distributing gives \( 3x - 12 = 18 \).
- Then, adding 12 gives \( 3x = 30 \).
- Finally, dividing by 3 gives \( x = 10 \).
- This method works correctly.

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

4. **First, multiply by 1.3 then subtract 4:**
- This step doesn't appropriately manipulate the given equation according to the algebraic principles that preserve equality (since multiplying by 1.3 is not the same as dividing by 3).
- This method would not yield the correct answer.

From the above analysis, the methods that correctly solve the equation are:

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

Both of these methods yield the correct answer of \( x = 10 \).

Answer 3

The methods that would also result in the correct answer are:

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

Both of these methods yield the correct solution \( x = 10 \). If you are looking for just one of them, you can choose either.

However, if you have to select only one option based on your original question, **the first option**: **"First distribute the 3, then add 4, and lastly divide by 3"** works.