How do you solve #x/(x-2)>9#?

1 Answer
Feb 23, 2017

Answer:

The solution is #x in ]2,9/4[#

Explanation:

We cannot do crossing over.

We rearrange the equation

#x/(x-2)>9#

#x/(x-2)-9>0#

#(x-9(x-2))/(x-2)>0#

#(x-9x+18)/(x-2)>0#

#(18-8x)/(x-2)>0#

#(2(9-4x))/(x-2)>0#

Let #f(x)=(2(9-4x))/(x-2)#

The domain of #f(x)# is #D_f(x)=RR-{2}#

We can build the sign chart

#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaaaa)##2##color(white)(aaaaaaaa)##9/4##color(white)(aaaa)##+oo#

#color(white)(aaaa)##x-2##color(white)(aaaa)##-##color(white)(aaaa)##||##color(white)(aaaa)##+##color(white)(aaaa)##+#

#color(white)(aaaa)##9-4x##color(white)(aaa)##+##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 ]2,9/4[#