How do you solve #(x+1)(x-7)<=0# using a sign chart?

1 Answer
Feb 19, 2017

Answer:

The solution is #x in [-1,7]#

Explanation:

Let #f(x)=(x+1)(x-7)#

Now, we build the sign chart

#color(white)(aaaa)##x##color(white)(aaaaa)##-oo##color(white)(aaaa)##-1##color(white)(aaaa)##7##color(white)(aaaa)##+oo#

#color(white)(aaaa)##x+1##color(white)(aaaaaa)##-##color(white)(aaaa)##+##color(white)(aaaa)##+#

#color(white)(aaaa)##x-7##color(white)(aaaaaa)##-##color(white)(aaaa)##-##color(white)(aaaa)##+#

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

Therefore,

#f(x)<=0# when #x in [-1,7]#