Question

One method for solving 3(x−4)=18
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, divide by 3, then subtract 4.
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 4, and lastly divide by 3.

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

First, multiply by 1/3
1
3
, then subtract 4.

Answer 1

choose one

Answer 2

Let's analyze the given equation step by step:

The equation is \( 3(x - 4) = 18 \).

1. **Divide by 3:**
\[ x - 4 = \frac{18}{3} \]
\[ x - 4 = 6 \]
2. **Add 4:**
\[ x = 6 + 4 \]
\[ x = 10 \]

Now, let's evaluate each of the methods provided to see if they will lead to the same solution \( x = 10 \).

1. **First, divide by 3, then subtract 4:**
\[ \frac{3(x - 4)}{3} = \frac{18}{3} \]
\[ x - 4 = 6 \]
\[ x = 6 + 4 \]
(This is just a rearrangement of the original method, which will not yield the correct answer.)

2. **First, distribute the 3, then add 4, and lastly divide by 3:**
\[ 3(x - 4) = 18 \]
\[ 3x - 12 = 18 \]
Add 12:
\[ 3x = 30 \]
Divide by 3:
\[ x = 10 \]
(This method works.)

3. **First, distribute the 3, then add 12, and lastly divide by 3:**
This method does not work as it would imply:
\[ 3x - 12 + 12 = 18 \]
So:
\[ 3x = 18 \]
Divide by 3:
\[ x = 6 \]
(This method does not work.)

4. **First, multiply by \( \frac{1}{3} \), then subtract 4:**
\[ \frac{1}{3}(3(x - 4)) = \frac{1}{3}(18) \]
This simplifies to:
\[ x - 4 = 6 \]
Add 4:
\[ x = 10 \]
(This method works.)

Among the methods presented, the second and the fourth methods will result in the correct answer of \( x = 10 \). Therefore, the correct choices are:

- **First, distribute the 3, then add 4, and lastly divide by 3.**
- **First, multiply by \( \frac{1}{3} \), then subtract 4.**

Answer 3

The correct choice that would also result in the correct answer is:

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