How do you solve #3/(x+1)<=3# using a sign chart?

1 Answer
Jun 22, 2017

Answer:

The solution is #x in (-oo,-1) uu [0,+oo)#

Explanation:

We cannot do crossing over

Let's rearrange the inequality

#3/(x+1)<=3#

#3/(x+1)-3<=0#

#(3-3x-3)/(x+1)<=0#

#(-3x)/(x+1)<=0#

Let #f(x)=(-3x)/(x+1)#

Let's build the sign chart

#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaaaa)##-1##color(white)(aaaaaaaa)##0##color(white)(aaaaa)##+oo#

#color(white)(aaaa)##-3x##color(white)(aaaaaa)##+##color(white)(aaaa)##||##color(white)(aaaa)##+##color(white)(aa)##0##color(white)(aa)##-#

#color(white)(aaaa)##x+1##color(white)(aaaaa)##-##color(white)(aaaa)##||##color(white)(aaaa)##+##color(white)(aa)##0##color(white)(aa)##+#

#color(white)(aaaa)##f(x)##color(white)(aaaaaa)##-##color(white)(aaaa)##||##color(white)(aaaa)##+##color(white)(aa)##0##color(white)(aa)##-#

Therefore,

#f(x)<=0# when #x in (-oo,-1) uu [0,+oo)# graph{3/(x+1)-3 [-19.3, 21.26, -12.45, 7.82]}