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x ~> 1

What is the limit as x approaches 1 of f(x)?

(Hint: let g(x) = [f(x) - 8] / [x - 1])

i'm not sure how the hint helps me in solving this problem. all i did was multiply both sides of the equation [f(x) - 8] / [x - 1] = 10 by (x - 1) and then added 8 to solve for f(x). then i got f(x) = 10x - 2 and i found that the limit of f(x) as x approaches 1 is 8. is that right? i just kinda guessed on how to do this problem. i don't really understand it.