SOLUTION: Solve the inequality and graph the solution set on a number line. Be sure to use closed dots or open circles. Do not use parentheses or brackets. (x+4)/(x-3)<=0

Algebra ->  Test -> SOLUTION: Solve the inequality and graph the solution set on a number line. Be sure to use closed dots or open circles. Do not use parentheses or brackets. (x+4)/(x-3)<=0       Log On


   

Question 1052677: Solve the inequality and graph the solution set on a number line. Be sure to use closed dots or open circles. Do not use parentheses or brackets.
(x+4)/(x-3)<=0
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Choose the critical points from the left hand side.
x=-4 and x=3
Breakj up the number line into 3 regions:
R1:x%3C-4
R2:-4%3Cx%3C3
R3:x%3E3
For each region, choose a point in the region (not an endpoint),
Test the inequality in the region.
R1: x=-5
%28-5%2B4%29%28-5-3%29%3C=0
%28-1%29%28-8%29%3C=0
8%3C=0
False, R1 is not part of the solution.
R2: x=0
%280%2B4%29%280-3%29%3C=0
%284%29%28-3%29%3C=0
-12%3C=0
True, R2 is part of the solution.
R3: x=4
%284%2B4%29%284-3%29%3C=0
%288%29%281%29%3C=0
8%3C=0
False, R3 is not part of the solution.
So then the solution is,
[-4,3)
You cannot include x=3 in the solution since the function is not defined at that point.
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