Question 82821: this question is not from the book even though i put in the imformation. its from a worksheet that we were given in class. and i know this is kind of something i should already know but i have missed a few classes and i still dont get how write infinities and unions. the question is:
(x-5)(x+4)(1-x)<0
i have looked over the book for help and think that it might be something to the effect of (-4,-1) U (5,infinity)
am i on the right track? could someone please tell me?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! (x-5)(x+4)(1-x)<0
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To do problems like this you have to first of all
find the values of x that make the left side zero.
They are x=5,x=-4, and x=1.
Then, draw a number line and find points
left to right of -4,1,5.
Those points break the number line into four intervals.
You have to check a test point from each interval to see
where the inequality is satisfied:
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In (-inf,-4) pick x=-100; then f(-100) is -*-*+ >0; so (-inf,-4) is not part of the solution.
In (-4,1) pick x=0; then f(0) is -*+*+ <0; so (-4,1) is part of the solution.
In (1,5) pick x=3; then f(3) is -*+*- >0; so (1,5) is not part of the solution.
In (5,inf) pick x=100; then f(100) is +*+*- <0; so (5,inf) is part of the solution.
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Final Answer (-4,1) U (5,inf)
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You have it right.
Cheers,
Stan H.
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