If (x-1)(x-4)>0, why is x<1 ?

If (x-1)(x-4)>0, why is x

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Have a look at the graph of this.....

Note, that we have three intervals of interest in this quadratic inequality.....

Namely, everything < 1, everything between 1 and 4, and everything > 4.

Note that all values between 1 and 4, inclusive, make this inequality untrue. For example, if x = 2, we have

(2-1)(2-4) = (1)(-2) = -2, and that's not greater than 0. Note that 1 and 4 don't work, either. They make the equality = 0, but it has to be >0.

So, the solutions to this inequality are .....x < 1    and x > 4