How do you solve x/(x-5) >= -2 ?

3 Answers
Mar 24, 2018

x>=10/3

Explanation:

x/(x-5) >=-2
x >= -2(x-5)
x>= -2x + 10
3x>=10
x>=10/3

Mar 24, 2018

x>=10/3

Explanation:

x>=-2(x-5) multiply both sides by x-5 to get rid of fraction
x>=-2x+10 distribute
3x>=10 add 2x to both sides
x>=10/3

Mar 24, 2018

x<=10/3 or x>5

Explanation:

x/(x-5)>=-2

We wanna find the critical points of the inequality

x/(x-5)=-2

Cross multiply

x = (-2)(x) + (-2)(-5)

x= -2x + 10

Add 2x on both sides

x + 2x = -2x + 10 + 2x

3x = 10

Then divide both sides by 3

(cancel3x)/(cancel3)=10/3

x=10/3

Don't forget we were looking for the critical points:

Critical points

x=10/3 which makes both sides equal

x=5

Ok now we can check the intervals in between critical points.

We have x<= 10/3 which works in the original inequality

We also have 10/3 <= x <5 which doesn't work in the original
inequality

And we have x > 5 which works in the original inequality

Thus,

The answers are:

x <= 10/3 or x > 5