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)

Question

Responses

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

Answer 1

To solve the equation \(3(x - 4) = 18\) correctly, you can use the method stated in your first option (divide by 3, then add 4).

Let's evaluate the alternatives one by one:

1. First, multiply by 13, then subtract 4.
   This would not work because the operations apply in a way that doesn't lead to isolating \(x\) correctly.

2. First, multiply by \( \frac{1}{3} \), then subtract 4.
   This also does not isolate \(x\) correctly, as multiplying by \( \frac{1}{3} \) would not correctly follow the order of operations needed to solve the equation.

3. First, distribute the 3, then add 4, and lastly divide by 3.
   Distributing the 3 gives \(3x - 12 = 18\). After distributing, we would need to add 12, not 4, to maintain equality, so this option is incorrect.

4. First, distribute the 3, then add 12, and lastly divide by 3.
   This is correct. Distributing gives \(3x - 12 = 18\), adding 12 results in \(3x = 30\), and dividing by 3 gives \(x = 10\).

5. First, divide by 3, then subtract 4.
   This method was already mentioned and is correct because after dividing \(3(x - 4) = 18\) by 3, you get \(x - 4 = 6\), and adding 4 yields \(x = 10\).

Thus, the correct alternative method is:

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