How do you solve #(x-7)/(x-1)<0#?

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Answer 1 · 2017-05-17T05:02:46

The solution is # x in (1,7)#

Let #f(x)=(x-7)/(x-1)#

The domain of #f(x)# is #D_f(x)=RR-{1}#

We build a sign chart

#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaaaa)##1##color(white)(aaaaaaaa)##7##color(white)(aaaa)##+oo#

#color(white)(aaaa)##x-1##color(white)(aaaa)##-##color(white)(aaaa)##||##color(white)(aaaa)##+##color(white)(aaaa)##+#

#color(white)(aaaa)##x-7##color(white)(aaaa)##-##color(white)(aaaa)##||##color(white)(aaaa)##-##color(white)(aaaa)##+#

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

Therefore,

#f(x)<0# when # x in (1,7)#