HELP with this inequality please??? :\

5/x-9 < 9/8x-7

This one is a little bit too complicated for me so if anyone could explain it please?

Did you mean 5/(x-9)< 9/(8x-7)
If so get zero on one side, then get a common denominator.
5/(x-9)-9/(8x-7)<0
[5(8x-7)-9(x-9)]/[(x-9)(8x-7)]<0
(31x+46)/[(x-9)(8x-7)] <0
there are three factors to solve
-46/31, 9, and 7/8
Put these on a number line and test the four parts of the line
......-46/31.........7/8........9.....…
Use any number in each part to test
At -10, the fraction will be (-)/(-)(-) so less than zero
At 0, the fraction will be (+)/(-)(-) so greater than zero
At 2, (+)/(-)(+), so less than zero
At 10, all +, so greater than zero
Therefore the solution is x < -46/31 or 7/8
-

Well now, assuming 5/x-9 < 9/8x-7 is actually 5/(x-9) < 9/(8x-7) --->

5(8x-7)< 9(x-9) ---> 40x-35 < 9x-81 ---> 31x < - 46 ---> x < - 46/31

or .....

If 5/x-9 < 9/8x-7 = (5/x)-9 < (9/(8x))-7 --->

5/x < (9/(8x)) + 2 ---> 5 < 9/8 + 2x ---> -31/8 < 2x ---> x > -31/16

If not, then rephrase your expression!

-

5/x-9 < 9/8x-7

5/x - 9/8x< 2

40 / 8x - 9 /8x <2

31 / 8x < 2

31 / 16 < x

or

x > 31 / 16 ---answer