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

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

First, divide by 3, then subtract 4.

Answer 1

To solve the equation \(3(x−4)=18\), one correct method is to divide both sides by 3 and then add 4, as you've mentioned.

Let’s analyze the options given:

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

   • Distributing the 3 gives \(3x - 12 = 18\). Adding 12 gives \(3x = 30\), and dividing by 3 gives \(x = 10\). This method works.

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

   • Distributing gives \(3x - 12 = 18\). Adding 4 makes it \(3x - 8 = 18\), which will not lead to the correct solution. This method does not work.

3. First, multiply by 13 then subtract 4.

   • This is irrelevant and does not relate to the initial equation correctly. This method does not work.

4. First, multiply by \(\frac{1}{3}\), then subtract 4.

   • Multiplying by \(\frac{1}{3}\) gives \(x - 4 = 6\). Then subtracting 4 gives \(x = 2\), which is incorrect. This method does not work.

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

   • Dividing gives \(x - 4 = 6\). Subtracting 4 gives \(x = 2\), which is also incorrect. This method does not work.

So the only method from your options that would also yield the correct answer is: First, distribute the 3, then add 12, and lastly divide by 3.