How do you solve #(x+2)/(x+5)>=1# using a sign chart?

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Answer 1 · 2016-11-28T07:12:16

The answer is #x in ] -oo,-5 [#

Let's rewrite the equation as

#f(x)=(x+2)/(x+5)-1>=0#

#f(x)=((x+2)-(x+5))/(x+5)>=0#

#f(x)=(x+2-x-5)/(x+5)=-3/(x+5)>=0#

The domain of #f(x)# is #D_f(x)=RR-{-5}#

Let's do the sign chart

#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaa)##-5##color(white)(aaaa)##+oo#

#color(white)(a)##-(x+5)##color(white)(aaaa)##+##color(white)(aaaaa)##-#

#color(white)(aaaa)##f(x)##color(white)(aaaaa)##+##color(white)(aaaaa)##-#

Therefore,

#f(x>=0)# when #x in ] -oo,-5 [ #

graph{-3/(x+5) [-18.99, 6.32, -6.33, 6.33]}