In the equation 3a + 2 = a(x - 3), what is the solution for a?

To solve the equation 3a + 2 = a(x - 3) for a, we first want to isolate a on one side.

Start by distributing the a on the right side:

3a + 2 = ax - 3a.

Next, to combine the a terms, move all the terms involving a to one side:

3a + 3a = ax - 2.

This simplifies to:

6a = ax - 2.

Now, we can isolate a by getting all terms with a on one side and constant terms on the other:

6a - ax = -2.

Factor out a from the left side:

a(6 - x) = -2.

Now, solve for a by dividing both sides by (6 - x):

a = -2 / (6 - x).

For simplicity, rewriting (6 - x) as -(x - 6) allows us to express a positively:

a = 2 / (x - 6).

This matches with the answer choice provided. Thus, the solution to the equation for a is 2/(x - 6).