Question 544173: Please help me understand this. Thanks!
Solve in interval notation
(x + 1)/(x-4) ≤ 0
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Please help me understand this. Thanks!
Solve in interval notation
(x + 1)/(x-4) ≤ 0
**
set factors=0, then solve for x
x+1=0
x=-1
x-4=0
x=4
critical points are -1 and 4
draw a number line with critical points on it
<...+...-1...-....4....+....>
solution in interval notation:
[-1,4] (includes -1 and 4)
..
Explanation for number line:
It is easily seen that for x>4, the function>0. Moving to the left, the sign of each interval switches when we go thru a critical x of odd multiplicity like 1, 3, 5, etc. Given x's are all of multiplicity 1.
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