To solve the equation \(3(x - 4) = 18\), you can indeed divide by 3 and then add 4, resulting in the solution. Letβs analyze the other methods you proposed to see if they would yield the correct solution.
-
First, multiply by \(\frac{1}{3}\), then subtract 4.
- Multiply both sides by \(\frac{1}{3}\): \((x - 4) = 6\)
- Then subtract 4: \(x = 10\) (This method is valid and results in the correct answer.)
-
First, distribute the 3, then add 4, and lastly divide by 3.
- Distributing gives: \(3x - 12 = 18\)
- Adding 12: \(3x = 30\)
- Dividing by 3: \(x = 10\) (This method is valid and results in the correct answer.)
-
First, divide by 3, then subtract 4.
- Dividing gives: \(x - 4 = 6\)
- Then subtracting gives: \(x = 6 + 4 = 10\) (This method is valid and results in the correct answer.)
-
First, distribute the 3, then add 12, and lastly divide by 3.
- Distributing gives: \(3x - 12 = 18\)
- Adding 12: \(3x = 30\)
- Dividing by 3: \(x = 10\) (This method is valid and results in the correct answer.)
All methods except for the first (multiply by \(\frac{1}{3}\) then subtract 4) are valid and lead to the same solution: \(x = 10\). Thus, the first method is indeed an example of an alternative that works.
The final options that yield the correct solution are:
- First, divide by 3, then subtract 4.
- First, distribute the 3, then add 12, and lastly divide by 3.
These will lead to the correct solution for the equation.