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?
Responses

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, divide by 3, then subtract 4.

First, multiply by 13, then subtract 4

Answer 1

To solve the equation \(3(x-4)=18\), let's explore the options provided. The goal is to manipulate the equation in different ways but still arrive at the correct solution for \(x\).

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

   • Distributing gives: \(3x - 12 = 18\).
   • Adding 12 to both sides: \(3x = 30\).
   • Dividing by 3: \(x = 10\).
   • This is a correct method.

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

   • Distributing gives: \(3x - 12 = 18\).
   • Adding 4 to both sides: \(3x - 12 + 4\) does not result in a correct simplification to reach \(x\).
   • This method does not work.

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

   • Dividing gives: \(x - 4 = 6\) (since \(18 \div 3 = 6\)).
   • Then, adding 4: \(x = 10\).
   • This is a correct method.

4. First, multiply by 13, then subtract 4.

   • Multiplying gives: \(39(x−4) = 234\), but that manipulates the equation incorrectly and does not yield the original equation.
   • This method does not work.

Thus, the methods that would also result in the correct answer are:

• First, distribute the 3, then add 12, and lastly divide by 3.
• First, divide by 3, then subtract 4.