How do you solve #(-2x+5)/(x+6)> -2# using a sign chart?

1 Answer
Jul 14, 2017

Answer:

The solution is #x in (-6,+oo)#

Explanation:

We cannot do crossing over, let's do some simplifications

#(-2x+5)/(x+6)>-2#

#(5-2x)/(x+6)+2>0#

#(5-2x+2x+12)/(x+6)>0#

#17/(x+6)>0#

Let #f(x)=17/(x+6)#

Let 's build the sign chart

#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaa)##-6##color(white)(aaaa)##+oo#

#color(white)(aaaa)##x+6##color(white)(aaaaa)##-##color(white)(aaaaa)##+#

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

Therefore,

#f(x)>0# when #x in (-6,+oo)#

graph{17/(x+6) [-32.46, 32.48, -16.24, 16.25]}