In order to be greater than 5, must be certainly be greater than 0 so 2x-3 ispositive. That means that we can just multiply both sides of the inequality by it to get 1> 5(2x- 3)= 10x- 15. That should be easy to solve.

That was easy because it was clear that the denominator must e positive to satisfy the inequality but usually we cannot be sure of that. More generally, the simplest way to solve complicated inequalities is to first solve the associatedequality- here, . Solving that is also easy: multiplying both sides by 2x- 3, 1= 5(2x- 3). 10x- 15= 1 gives 10x= 16 so x= 16/10= 8/5.

The point of that is that such an inequality can "swap" directions only where the two sides areequalor where there is a "discontinuity". Rational functions are discontinuous only where the denominator is 0:here where 2x-3= 0 or x= 3/2. The two points at which the inqualitycanreverse are 3/2 and 8/5. They divide the real number line into three intervals. Checking a single point in each interval will tell you which is ">" and which is "<".