Question

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

Answer 1

To solve the equation \(3(x - 4) = 18\), you can use various methods, but they must adhere to the rules of arithmetic.

The original equation, \(3(x - 4) = 18\), can be simplified and solved in different ways. Here's a breakdown of the provided responses to determine which one will lead to the correct answer:

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

   • Distributing gives \(3x - 12 = 18\), then adding 12 results in \(3x = 30\), and dividing by 3 gives \(x = 10\). This method works.

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

   • This method does not correctly isolate the variable. It leads to an incorrect result, so this method does not work.

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

   • This method also incorrectly manipulates the equation and does not yield the correct result, so this method does not work.

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

   • Dividing by 3 gives \(x - 4 = 6\), then subtracting 4 results in \(x = 2\). This method does not work.

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

   • This effectively does the same as dividing by 3. It results in \(x - 4 = 6\), and subtracting 4 results in \(x = 2\). This method does not work.

Looking at the evaluations, the only correct method that results in the right value of \(x\) is the first response: "First, distribute the 3, then add 12, and lastly divide by 3."

So, the correct answer is: First, distribute the 3, then add 12, and lastly divide by 3.