How do you solve #(x-4)/(x+3)<=0# using a sign chart?

1 Answer
Nov 12, 2016

Answer:

The answer is #x in ]-3,4]#

Explanation:

As you canot divide by #0#, therefore #x!=-3#

Let #f(x)=(x-4)/(x+3)#

let's do the sign chart

#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaa)##-3##color(white)(aaaaa)##4##color(white)(aaaaa)##+oo#

#color(white)(aaaa)##x+3##color(white)(aaa)##-##color(white)(aaaa)##∣∣##color(white)(aa)##+##color(white)(aaaa)##+#

#color(white)(aaaa)##x-4##color(white)(aaa)##-##color(white)(aaaa)##∣∣##color(white)(aa)##-##color(white)(aaaa)##+#

#color(white)(aaaa)##f(x)##color(white)(aaaa)##+##color(white)(aaaa)##∣∣##color(white)(aa)##-##color(white)(aaaa)##+#

Therefore, #f(x)<=0# #=>##x in ]-3,4]#
graph{(x-4)/(x+3) [-32.46, 32.46, -16.24, 16.25]}