Factorial Equation Problem

[maroonblazer]

I'm struggling to solve for x in the following:



Do I multiply each side by

Thanks in advance,
mb

[nona.m.nona]

Do I multiply each side by

You could do that, or multiply through by the larger denominator in order to get a linear equation.

Do the brackets indicate the "floor" or "ceiling" function, or something else? Thank you.

[maroonblazer]

You could do that, or multiply through by the larger denominator in order to get a linear equation.

Thanks for your reply! I was using the brackets to separate the factorials. I've edited the question so it's clearer.

So following that approach I get:





...I've done something wrong by this point because the answer is supposed to be 15 and this isn't headed in that direction.

Help?

[nona.m.nona]

...I've done something wrong by this point because the answer is supposed to be 15 and this isn't headed in that direction.

My apologies: For factorials, of course (x - 7)! is larger than (x - 8)!, because (x - 7)! = 1*2*3*...*(x - 9)*(x - 8)*(x - 7), while (x - 8)! = 1*2*3*...*(x - 9)(x - 8).

Start from your first equation in your last post, noting that (x - 8)! / (x - 7)! = 1/(x - 7).

[maroonblazer]

...I've done something wrong by this point because the answer is supposed to be 15 and this isn't headed in that direction.

My apologies: For factorials, of course (x - 7)! is larger than (x - 8)!, because (x - 7)! = 1*2*3*...*(x - 9)*(x - 8)*(x - 7), while (x - 8)! = 1*2*3*...*(x - 9)(x - 8).

Start from your first equation in your last post, noting that (x - 8)! / (x - 7)! = 1/(x - 7).

Got it! Thanks very much!!