One method for solving 3(x−4)=18

Question

is to first divide by 3, then add 4. Which method below would also result in the correct answer?(1 point)
Responses

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

First, multiply by 13
, then subtract 4.

Answer 1

To solve the equation \( 3(x - 4) = 18 \), we want to look for other valid operations that will ultimately yield the same value of \( x \).

1. Starting with the original method, divide both sides by 3: \[ x - 4 = 6 \] Then add 4: \[ x = 10 \]

Now let's evaluate each response to see if they also lead to the solution \( x = 10 \):

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

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

3. First, divide by 3, then subtract 4. \[ 3(x - 4) = 18 \implies x - 4 = 6 \implies x = 10. \] This method works.

4. First, multiply by 13, then subtract 4. This does not make sense in the context of this equation since multiplying by 13 doesn’t preserve the equality: \[ 3(x - 4) \implies 39(x - 4) \text{ would not lead to a solution that relates to the original equation.} \] Thus, this method does not work.

From the analysis, the methods that lead to the correct answer \( x = 10 \) 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.
• First, divide by 3, then subtract 4.

The correct answer choices are either of the first three methods listed above.