A question like this on the SAT will always have answer choices, and in this case would be easy to backsolve. Don’t rob yourself of easy points—remember that answer choices are often a helpful tool! Use them to your advantage. In this case, you’d simply need to plug (2x – 1) in for x in each answer choice until one gave you cx.
Since you didn’t provide answer choices, though, we’ll have to do this the hard way.
The way I like to think about questions like this is pretty procedural. You’ve got some f(x) expression. You swap out the x for (2x – 1) and what happens? First, the 2x means there’s a doubling. We know we want to land on cx, so f(x) must have a c/2 in the x term that gets doubled. Make sense?
But what about those question marks? Well, we know that the end result we want is that f(2x – 1) = cx, so that question mark must cancel out the –c/2 we get from multiplying c/2 by (2x – 1). What cancels out –c/2? Easy: +c/2! So let’s see if making f(x) = (c/2)x + c/2 works:
Yep, that works. Again, it probably would have been easier to just start with the answer choices and see which one landed you on cx. Your work would end up looking just like that second bit of math above, but without so much abstract thinking required.
Draw this to make sure you don’t get messed up. Let’s use X for all the people in line who aren’t Bill and B for Bill.
X X X X B X X X X X X X X X X X
Above, Bill is the 5th person from the left and the 12th person from the right–that means there are 4 people to the left of him and 11 people to the right of him. 4 + 11 + 1 for Bill is 16 people in line, total.