How do you solve and write the following in interval notation: #(x + 4)(x − 5)(x + 6) ≥ 0#?

1 Answer
Jul 11, 2017

Answer:

The solution is #x in [-6,-4] uu [5, +oo)#

Explanation:

Let #f(x)=(x+4)(x-5)(x+6)#

We build a sign chart

#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaa)##-6##color(white)(aaaaa)##-4##color(white)(aaaaaaa)##5##color(white)(aaaaa)##+oo#

#color(white)(aaaa)##x+6##color(white)(aaaaa)##-##color(white)(aa)##0##color(white)(aaa)##+##color(white)(aaaaa)##+##color(white)(aaaaa)##+#

#color(white)(aaaa)##x+4##color(white)(aaaaa)##-##color(white)(aaaaaa)##-##color(white)(aa)##0##color(white)(aa)##+##color(white)(aaaaa)##+#

#color(white)(aaaa)##x-5##color(white)(aaaaa)##-##color(white)(aaaaaa)##-##color(white)(aaaaa)##-##color(white)(aa)##0##color(white)(aa)##+#

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

Therefore,

#f(x)>=0# when #x in [-6,-4] uu [5, +oo)#

graph{(x+4)(x-5)(x+6) [-44.86, 47.6, -31.26, 15]}