How do you solve the inequality: #(x - 3) (x - 5) > 0#?

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Answer 1 · 2015-08-28T14:13:37

#x in (-oo, 3) uu (5, +oo)#

In order for this inequality to be true, you need #(x-3)# and #(x-5)# to either both be positive or both be negative.

For any value of #x>5# you will get

#{(x-3 > 0), (x-5>0) :} implies (x-3)(x-5)>0#

For any value of #x<3# you will get

#{(x-3<0), (x-5<0):} implies (x-3)(x-5)>0#

This inequality will thus be satisfied for any value of #x in (-oo, 3) uu (5, +oo)#.

On the other hand, any value of #x in [3, 5]# will not be a valid solution.