Order equivalent equations of 2(x – 3) = 4x to solve for x.

To solve the equation (2(x – 3) = 4x), let’s first simplify it step by step:

1. Distribute the 2:

[

2x – 6 = 4x

]

2. Rearrange the equation:

Subtract (2x) from both sides:

[

-6 = 4x – 2x

]

This simplifies to:

[

-6 = 2x

]

3. Divide both sides by 2 to isolate (x):

[

x = -3

]

Now, let’s check the equivalent equations provided:

– (2x – 6 = 4x) is correct.

– (-3 = 2x) can be rearranged to get (x = -3); this is also correct.

– (-3 = x) is not equivalent, as we found (x = -3) but this format isn’t foundationally sound since it suggests a contradiction.

– (-6 = 2x) is correct and leads to the same conclusion.

– (2x – 3 = 4x) does not hold true based on the original equation as it’s derived differently.

– (-frac{3}{2} = x) is incorrect based on the solved value.

Therefore, the correct