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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?(1 point)
Responses

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.
First, divide by 3, then subtract 4.

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.
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1 answer

To solve the equation \( 3(x - 4) = 18 \), we can use different methods that manipulate the equation but still follow algebraic principles.

The original method you provided involves dividing by 3 first and then adding 4.

Let’s analyze each of the provided options:

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

    • This is not correct because it does not maintain the equivalence of the equation.

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

    • This is not correct because multiplying by \( \frac{1}{3} \) would give \( x - 4 = 6 \), and then subtracting 4 would not solve for \( x \) correctly.

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

    • This option essentially breaks down to the original method since it starts correctly with division, but the step of subtracting 4 instead of adding will give an incorrect result.

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

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

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

    • This option is incorrect because adding 4 after distributing will not give the correct result.

Thus, the correct answer is:

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