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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?

First divide by 3, then subtract 4

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, multiply by 1.3 then subtract 4

3 answers

To solve the equation \( 3(x - 4) = 18 \), we can check which of the proposed methods will also lead to the correct solution.

  1. First divide by 3, then subtract 4:

    • Dividing both sides by 3 gives \( x - 4 = 6 \).
    • Then, subtracting 4 gives \( x = 6 + 4 = 10 \).
    • This method does not yield the correct answer, as \( x - 4 \) should equal 6 and we need to add 4, not subtract it.

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

    • Distributing gives \( 3x - 12 = 18 \).
    • Then, adding 12 gives \( 3x = 30 \).
    • Finally, dividing by 3 gives \( x = 10 \).
    • This method works correctly.

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

    • Distributing gives \( 3x - 12 = 18 \).
    • Adding 12 gives \( 3x = 30 \).
    • Dividing by 3 gives \( x = 10 \).
    • This method also works correctly.

  4. First, multiply by 1.3 then subtract 4:

    • This step doesn't appropriately manipulate the given equation according to the algebraic principles that preserve equality (since multiplying by 1.3 is not the same as dividing by 3).
    • This method would not yield the correct answer.

From the above analysis, the methods that correctly solve the equation 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 of these methods yield the correct answer of \( x = 10 \).

So which one

The methods that would also result in the correct answer are:

  1. First distribute the 3, then add 4, and lastly divide by 3.
  2. First distribute the 3, then add 12 and lastly divide by 3.

Both of these methods yield the correct solution \( x = 10 \). If you are looking for just one of them, you can choose either.

However, if you have to select only one option based on your original question, the first option: "First distribute the 3, then add 4, and lastly divide by 3" works.