SOLUTION: 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.

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
***
(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)
RELATED QUESTIONS
Solve the inequality. Express the solution using interval notation and graph the solution (answered by MathLover1)

Solve the inequality algebraically. Express the solution using interval notation and... (answered by tommyt3rd)

solve the rational inequality and graph the solution set on a real number line. Express... (answered by oscargut)

Solve the rational inequality and graph the solution set on a real number line. Express... (answered by stanbon)

solve the polynomial inequality and graph the solution set on a real number line. Express (answered by robertb)

Solve the polynomial inequality and graph the solution set on a real number line. Express (answered by lwsshak3)

Solve the inequality. Write the solution set using interval notation and graph the... (answered by Boreal)

solvethe rational inequality and graph the solution set on a real number line. express... (answered by Fombitz)

Solve the inequality, graph the solution set on the real number line, and then write the... (answered by sofiyac)