Question 484280: Solve the inequality. Express the solution using interval notation and graph the solution set on the real number line.
1) (5/x^3-x^2-4x+4)<0.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Solve the inequality. Express the solution using interval notation and graph the solution set on the real number line.
1) (5/x^3-x^2-4x+4)<0
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(5/x^3-x^2-4x+4)<0
5/x2(x-1)-4(x-1)<0
5/(x-1)(x^2-4)<0
5/(x-1)(x+2)(x-2)<0
number line:
<....-...-2.....+.....1.....-.....2.....+......>
Explanation for number line:
By inspection, you can see that for x>2, the expression >0. Moving to the left, the sign of the intervals switch if we go thru roots that are of odd multiplicity, ie, 1, 3, 5, etc. In this case all the roots are of multiplicity 1.
solution:
(-∞,-2) U (1, 2)
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