Question 90031: I have one more problem please:
Solve the inequality and state and graph the solution set:
x^2-12x+27<0
Thank you very much!
Answer by yannick(6)   (Show Source):
You can put this solution on YOUR website! x^2-12x+27
by factoring the expression, we find,
x^2-12x+27 = (x-9)(x-3)
So (x-9)(x-3)< 0 means that
1) x-9<0 so, x<9
and
x-3>0 so, x>3
x<9 and x>3 mean that the solution1 s1 = (3,9)
by checking this solution by using x=4 (because zero is included between 3and 9), we come out with -65<0 so the solution1 is the solution.
2) x-9>0 so, x>9
and
x-3<0 so, x<3
s2=(-∞,3)U(9,+∞)
By checking S2 by using x=0, we come out with 27 that is not less than zero.
We're also checking S2 by using X=10, and we came out with 7 that is not less than zero too. so, s2 is not a solution.
Conclusion,
the inequality x^2-12x+27<0 has as solution S=(3,9)
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