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Solve the inequality?
State the range of values of "x" for which the inequality holds true
(x-4)^2005 . (x+8)^2008 . (x+1)
------------------------------------------------------------------- <=0
x^2006 . (x-2)^3 . (x+3)^5 . (x-6) (x+9)^2010
1 Answer
- vahucelLv 69 years agoFavourite answer
Find the roots of the numerator... it is x=4, x= -8 and x = -1
Find the discontinuities... the roots of denominator... it is x= -9, x= -3, x=2, x =6 .
Now put in order the roots and discontinuities in x-axis and study the signal of the function...
.....-9.....-8....-3......-1.....2 .....4 .....6..... To study the signal of the function just choose a value in each interval and put in the function to find the signal... it is
- - - - (-9) ++++(-8) - - - - (-3) + + + + (-1) - - - -(2) + + + + (4) - - - - (6) + + + + +
The answer is the intervals where the sign is negative... the descontinuities cannot be used.
The as is is <=0 the the answer are the intervals:
(-infinity, -9) or [-8. -3) or [-1, 2) or [4,6) ...... that can be written so:
x<-9 or -8 <=x <-3 or -1<=x<2 or 4<=x<6 OK!