How do solve $(x+2)/(x+5)>=1$ algebraically?

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Answer 1 · 2017-01-23T12:09:53

The answer is $x<-5$

Multiply LHS and RHS by $(x+5)^2$

Therefore,

$(x+2) / (x+5) * (x+5)^2>=1*(x+5)^2$

$(x+2)(x+5)>=(x+5)^2$

$(x+2)(x+5)-(x+5)^2>=0$

$(x^2+7x+10)-(x^2+10x+25)>=0$

$7x+10-10x-25>=0$

$-3x-15>=0$

$3x<=-15$

$x<=-5$

We have to remove the equal sign, as we divide by $0$

So,

$x<-5$

How do solve (x+2)/(x+5)>=1(x+2)/(x+5)>=1 algebraically?