How do you solve #(w-6)/w<=0# using a sign chart?

1 Answer
Jan 23, 2017

Answer:

The answer is #x in ]0,6]#

Explanation:

Let #f(w)=(w-6)/w#

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

Let's build the sign chart

#color(white)(aaaa)##w##color(white)(aaaa)##-oo##color(white)(aaaaa)##0##color(white)(aaaaa)##6##color(white)(aaaaaa)##+oo#

#color(white)(aaaa)##w##color(white)(aaaaaaaa)##-##color(white)(aa)##||##color(white)(aa)##+##color(white)(aaaa)##+#

#color(white)(aaaa)##w-6##color(white)(aaaaa)##-##color(white)(aa)##||##color(white)(aa)##-##color(white)(aaaa)##+#

#color(white)(aaaa)##f(w)##color(white)(aaaaaa)##+##color(white)(aa)##||##color(white)(aa)##-##color(white)(aaaa)##+#

Therefore,

#f(w)<=0# when #x in ]0,6]#