Question 397955: Solve (x+4)(x-9)(x+2)>0
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Solve (x+4)(x-9)(x+2)>0
Since the problem is already in factored form, the best way to do this is use a number line with the roots on it.
Starting from the left side, mark the line with the roots,-4, -2, and 9
we now have the following intervals from left to right:
(-infinity,-4),(-4,-2)(-2,9),(9,infinity)
note that when x is a very large number greater than 9, the (9,infinity) interval is positive. From here, going left on the number line, the signs of the following intervals switch signs, that is, (-2,9) interval is negative, (-4,-2) interval is positive,and the (-infinity,-4) interval is negative.(note: the signs switch when the roots are of an odd multiplicty(1,3,5 etc) They will not switch when roots are of even multiplicity (2,4,6, etc))
To satisfy the given equation only the x-values which give a positive output are valid. These x-values are in the positive intervals identified above.
ans: The x-values that satisfy the given equation are in the intervals, (-4,-2) and (9,infinity)
Instead of a number line you can use a chart to determine the signs of the intervals, but the number line is more efficient way to do this.
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