SOLUTION: solve the folowing inequation x+3/x-2 less than equal to 2 i have solved this in the following way x+3/ x-2 - 2 less than equal to 0 -x+7 / x-2 less than equal to 0 x-7/ x-2

Question 78080: solve the folowing inequation
x+3/x-2 less than equal to 2
i have solved this in the following way
x+3/ x-2 - 2 less than equal to 0
-x+7 / x-2 less than equal to 0
x-7/ x-2 greater than equal to 0
x belongs to (- infinity, 2 ) union [ 7, infinity)
SIR I CANNOT UNDERSTAND THIS FORM
x belongs to (- infinity, 2 ) union [ 7, infinity)

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
solve the folowing inequation
x+3/x-2 <= 2
--------------------------------
1st: Notice that x cannot be 2 because x-2 is in the denominator.
2nd: Solve the equality:
(x+3)/(x-2)=2
x+3 = 2x-4
x=7 (so that is a point in the solution set.
3rd:
Draw a line.
Plot the two values x=2 and x=7 on the line.
This breaks the line into three intervals ; pick a test point in each
interval to see where the solution set(s) lie.
--------
Interval (-inf,2); pick x=0; substitute into the inequality: 3/-2<2
that is true so the interval is part of the solution set.
------
Interval (2,7] ; pick x=5; substitute to get 8/3<2; false; no solutions here
--------
Interval [7,inf); pick x=10; substitute to get 13/8<2; true; solutions here.
==============
Final Answer:
x is an element of (-inf,2) OR [7,inf}
Cheers,
Stan H.
RELATED QUESTIONS
What positive integers satisfy -2 less than or equal to 3x - 4 less than or equal to 7? (answered by rfer)

how do i solve this inequality 2(x-3)is equal to or less than... (answered by lwsshak3)

Solve: (x+2)^3(x-1)^2(x-3) less than or equal to... (answered by josgarithmetic)

solve and graph the inequality. Can someone help me answer this? x+3/x less than or... (answered by rapaljer)

I don't know how to solve the following inequality: 3x-2 over x+3 is less than or equal... (answered by DrBeeee)

Can somone please tell me how to do this i am so confused. Let X be a random variable... (answered by stanbon)

If 0 degrees less than or equal to x less than or equal to 360 degrees, solve the... (answered by ad_alta)

1<= |x - 2| <= 3 <= means less than or equal to (answered by scott8148)

Please help me solve this equation: 2-3x is less than 5(2-x) is less than or equal to... (answered by josgarithmetic)