How do you solve #x^2<=9# using a sign chart?

1 Answer
Feb 8, 2017

Answer:

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

Explanation:

Let's rewrite the equation

#x^2<=9#

#x^2-9<=0#

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

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

Now, we can build the sign chart

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

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

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

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

Therefore,

#f(x)<=0# when #x in [-3,3]#