Question 902235: TABLE OF SIGNS
Suppose:
x + 10/(x − 17)^2 ≥ 0
Create a table of signs from this inequality.
Please explain how this is done. Because someone else poorly explained this process to me and now I feel way behind in my precalculus class.
Also:
Select the intervals below that can be combined to form the solution set for the given inequality.
NOTE: If the solution includes a interval such as ( -5 , 3 ], you should choose ONLY ( -5 , 3 ] and NOT ( -5 , 3 ).
(−∞, −10)
(−∞, −10]
[−10, 17)
[−10, 17]
(−10, 17)
(−10, 17 ]
(17, ∞)
[17, ∞)
(−10, ∞)
(−∞, 17)
[−10, ∞)
(−∞, 17]
Please explain how these are solved
THANK YOU
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! First for any rational inequality, find the critical points where the numerator or the denominator equal zero.
In this case,
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So now break up the number line into three regions based on these critical numbers.
Values where the denominator equals zero are values that are not in the domain of the function since division by zero is undefined.
So for those values use ().
Region 1 : ( , ]
Region 2 : [, )
Region 3 : (,)
For each region choose a point in the region (avoid the endpoints) and test the inequality.
If the inequality is satisfied, that region is part of the solution.
Otherwise, that region is not part of the solution.
Region 1 : Choose 
False, Region 1 is not part of the solution region.
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.
Region 2 : Choose 
True, Region 2 is part of the solution region.
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Region 3 : Choose 
True, Region 3 is part of the solution region.
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.
So the solution region is
[,)U (,)
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.
In terms of table of signs,
where LHS is Left Hand side of the equation, N is negative, P is positive.
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