Question 462450
{{{(3x+2)^100(5-x)^99/(2x-7)^101<=0}}}

The inequality is in standard form already (i.e., one side of the inequality is equal to zero).
The critical numbers are: 

-2/3, 7/2, and 5. 

({{{-infinity}}}, -2/3): {{{(3x+2)^100(5-x)^99/(2x-7)^101 < 0}}}.  (Choose test number x = -1.)

( -2/3, 7/2): {{{(3x+2)^100(5-x)^99/(2x-7)^101 < 0}}}.  (Choose test number x = 0).

(7/2, 5): {{{(3x+2)^100(5-x)^99/(2x-7)^101 > 0}}}.  (Choose test number x = 4.)


(5, {{{infinity}}}): {{{(3x+2)^100(5-x)^99/(2x-7)^101 < 0}}}.  (Choose test number x = 6.)

The critical numbers -2/3 and 5 also satisfy the inequality, but not 7/2.  Hence the solution set is the union

({{{-infinity}}}, 7/2) U [5, {{{infinity}}}).