How do you solve #(x+2)/x<=0# using a sign chart?

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Answer 1 · 2017-02-26T06:51:56

The answer is #x in [-2,0[#

Let #f(x)=(x+2)/x#

The domain of #f(x)# is #D_f(x)=RR-{0}#

We can build the sign chart

#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaa)##-2##color(white)(aaaaaaa)##0##color(white)(aaaaa)##+oo#

#color(white)(aaaa)##x+2##color(white)(aaaaa)##-##color(white)(aaaaa)##+##color(white)(aaa)##||##color(white)(aa)##+#

#color(white)(aaaa)##x##color(white)(aaaaaaaaa)##-##color(white)(aaaaa)##-##color(white)(aa)##||##color(white)(aa)##+#

#color(white)(aaaa)##f(x)##color(white)(aaaaaa)##+##color(white)(aaaaa)##-##color(white)(aaa)##||##color(white)(aa)##+#

Therefore

#f(x)<=0# when #x in [-2,0[#