How do you solve the inequality #-x^2-6x+7<=0#?

1 Answer
Jan 2, 2017

Answer:

The answer is # x in ] -oo,-7] uu [ 1, +oo[ #

Explanation:

Let`s rewrite the inequality

#x^2+6x-7>=0#

We factorise

#(x-1)(x+7)>=0#

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

The domain of #f(x)# is #D_f(x)=RR#

We do a sign chart

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

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

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

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

Therefore,

#f(x)>=0#, when # x in ] -oo,-7] uu [ 1, +oo[ #