For which m is the solution of the following sistem

0<x^2-5x+6 and mx-4<(2mx-5(x-m))/2

Is x<2?

First rearrange the second inquality.

mx-4< (2mx-5(x-m))/2 = (2mx -5x+5m)/2
mx-4 < mx -(5/2)x +5m/2
0 < (5/2)x + 5m/2 + 4
0 < x + m + (8/5) is equivalent to the second inequality.
The first inequality requires that
(x-6)(x+1) > 0
This is true for x>6 and x <-1
Both inequalities are satisfied if
-m -8/5 >6
m < 8 2/5