How do you solve #(-x+2)/(x-4)>=0#?

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Answer 1 · 2016-12-30T13:21:41

The answer is #x in [2, 4 [ #

Let #f(x)=(-x+2)/(x-4)#

The domain of #f(x)# is #D_f(x)=RR-{4} #

We have to make a sign chart

#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaaaa)##2##color(white)(aaaaaa)##4##color(white)(aaaaaa)##+oo#

#color(white)(aaaa)##2-x##color(white)(aaaaaa)##+##color(white)(aaaa)##-##color(white)(aa)##∥##color(white)(aa)##-#

#color(white)(aaaa)##x-4##color(white)(aaaaaa)##-##color(white)(aaaa)##-##color(white)(aa)##∥##color(white)(aa)##+#

#color(white)(aaaa)##f(x)##color(white)(aaaaaaa)##-##color(white)(aaaa)##+##color(white)(aa)##∥##color(white)(aa)##-#

Therefore,

#f(x)>=0# when # x in [2, 4 [ #