How do you solve #(5x-8)/(x-5)>=2# using a sign chart?

1 Answer
Feb 6, 2017

Answer:

The answer is #x in ]-oo, -2/3 ] uu ] 5, +oo[#

Explanation:

Let's do some simplifications

#(5x-8)/(x-5)>=2#

#(5x-8)/(x-5)-2>=0#

#((5x-8)-2(x-5))/(x-5)>=0#

#(3x+2)/(x-5)>=0#

Let #f(x)=(3x+2)/(x-5)#

Let's build the sign chart

#color(white)(aaaa)##x##color(white)(aaaaa)##-oo##color(white)(aaaa)##-2/3##color(white)(aaaa)##5##color(white)(aaaaa)##+oo#

#color(white)(aaaa)##3x+2##color(white)(aaaaaa)##-##color(white)(aaaa)##+##color(white)(aaaa)##+#

#color(white)(aaaa)##x-5##color(white)(aaaaaaa)##-##color(white)(aaaa)##-##color(white)(aaaa)##+#

#color(white)(aaaa)##f(x)##color(white)(aaaaaaaa)##+##color(white)(aaaa)##-##color(white)(aaaa)##+#

Therefore,

#f(x)>=0# when #x in ]-oo, -2/3 ] uu ] 5, +oo[#