Question 467364
Solve the inequality. Express your solution using interval notation and please show all of your work.
x(x + 6)(8 – x)≥ 0 
...
The best way I know how to show you how to find the solution is to first draw a number line with the zeros on it. (since function is already in factored form)

-∞............-6..........0............8...............∞
next, we need to determine the sign of the intervals between the zeros


Make a chart to determine signs of intervals:
x..........-.....-6......-......0......+........8.......+...........∞
(x+6)....-.....-6.....+......0.......+.......8........+..........∞
(x-8)....-.....-6.......-.....0.......-.......8........+..........∞
f(x)......-......-6......+.....0.......-.......8.........+.........∞

According to chart in interval notation:
solution: [6,0]  U  [8,∞)  (positive intervals)

note: I have not tried this format before. Let me know how you like it.