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, 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.

Answer 1

To solve the equation \(3(x - 4) = 18\), you can indeed divide by 3 and then add 4.

Let's analyze the options given:

1. **First, multiply by 13, then subtract 4.**
This does not lead to a solution relevant to the given equation, as it's not a valid operation for isolating the variable.

2. **First, multiply by \( \frac{1}{3} \), then subtract 4.**
This helps in dividing by 3 but not in isolating \( x \) correctly.

3. **First, divide by 3, then subtract 4.**
This would not result in the correct answer since subtracting 4 after dividing will not isolate x correctly.

4. **First, distribute the 3, then add 12, and lastly divide by 3.**
This option is a valid way to rearrange and simplify the equation. Distributing gives \( 3x - 12 = 18 \). Adding 12 results in \( 3x = 30 \), and then dividing by 3 gives \( x = 10 \).

5. **First, distribute the 3, then add 4, and lastly divide by 3.**
This does not lead to isolating \( x \) correctly as the addition does not align with the equation's balance.

From this analysis, the correct method resulting in the answer is:

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

This option correctly follows the steps to isolate \( x \).