math

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?

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  1. 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

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