SOLUTION: 2. Solve the inequality. Express your solution using interval notation and please show all of your work. x(x + 6)(8 – x)≥ 0

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Question 467357: 2. Solve the inequality. Express your solution using interval notation and please show all of your work.
x(x + 6)(8 – x)≥ 0
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The critical numbers are -6, 0, 8.
In the interval (-infinity, -6): x%28x+%2B+6%29%288-x%29%3E0. (Use the test number x = -7.)
In the interval (-6, 0): x%28x+%2B+6%29%288-x%29%3C0. (Use the test number x = -5.)
In the interval (0, 8): x%28x+%2B+6%29%288-x%29%3E0. (Use the test number x = 1.)
In the interval (8, infinity): x%28x+%2B+6%29%288-x%29%3C0. (Use the test number x = 9.)
The critical numbers themselves -6,0, and 8 satisfy the inequality. Hence the solution set is
(-infinity, -6]U [0, 8].