SOLUTION: Solve the inequality, and express the solutions in terms of intervals whenever possible. (x+2)(x-1)(4-x) which is less than or equal to 0

Question 496738: Solve the inequality, and express the solutions in terms of intervals whenever possible.
(x+2)(x-1)(4-x) which is less than or equal to 0

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Solve the inequality, and express the solutions in terms of intervals whenever possible.
(x+2)(x-1)(4-x) which is less than or equal to 0
**
(x+2)(x-1)(4-x)≤0
number line
<....+...-2.....-....1.....+.....4....-.....>
Interval notation:
(-∞,-2] U [1, 4]
..
Explanation for number line:
By inspection you can see that when x>4, the function becomes negative as shown.
Moving to the left thru the zeros, the sign of the interval will switch if the zeros are of an odd multiplicity, ie, 1, 3, 5, etc. For the given problem all the zeros are of multiplicity 1, thus the switch.
For math courses I have taken over the recent years, usually charts are used to determine the sign of the intervals, but I have found the method above to be much simpler and quicker.
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