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

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

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.

3 answers

To solve the equation \(3(x - 4) = 18\), one method involves dividing by 3 first and then adding 4, as stated in the question.

Let's analyze the proposed response methods to see which ones lead to the correct answer:

  1. First, distribute the 3, then add 4, and lastly divide by 3.
    Distributing gives \(3x - 12 = 18\). After that, you add 12 to both sides resulting in \(3x = 30\), and then dividing by 3 gives \(x = 10\). This results in the correct answer.

  2. First, multiply by \(\frac{1}{3}\), then subtract 4.
    Multiplying by \(\frac{1}{3}\) gives us \(x - 4 = 6\). To isolate \(x\), we would then add 4 (not subtract). Therefore, this method is incorrect.

  3. First, divide by 3, then subtract 4.
    Dividing gives \((x - 4) = 6\). Subtracting 4 would also not isolate \(x\) correctly. This method doesn't work.

  4. First, distribute the 3, then add 12, and lastly divide by 3.
    Distributing gives \(3x - 12 = 18\). Adding 12 results in \(3x = 30\), and dividing by 3 gives \(x = 10\). This method works and leads to the correct answer.

Thus, the methods that would also lead to the correct answer 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 methods 1 and 4 work correctly.

pick one.

I'll pick the first method:

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

This method correctly leads to the solution of the equation.