How do you solve and write the following in interval notation:#((x+8)(x-5) )/ (x-1) ≥ 0#?

1 Answer
Narad T.
Feb 26, 2017

The solution is #x in [-8,1 [uu [5, +oo [#

Explanation:

Let #f(x)=((x+8)(x-5))/(x-1)#

Let's build the sign chart

#color(white)(aaaa)##x##color(white)(aaaaaa)##-oo##color(white)(aaaa)##-8##color(white)(aaaaaaa)##1##color(white)(aaaaaaaa)##5##color(white)(aaaaaa)##+oo#

#color(white)(aaaa)##x+8##color(white)(aaaaaaa)##-##color(white)(aaaa)##+##color(white)(aaaa)##||##color(white)(aaaa)##+##color(white)(aaaaa)##+#

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

#color(white)(aaaa)##x-5##color(white)(aaaaaaa)##-##color(white)(aaaa)##-##color(white)(aaaa)##||##color(white)(aaaa)##-##color(white)(aaaaa)##+#

#color(white)(aaaa)##f(x)##color(white)(aaaaaaaa)##-##color(white)(aaaa)##+##color(white)(aaaa)##||##color(white)(aaaa)##-##color(white)(aaaaa)##+#

Therefore,

#f(x)>=0# when #x in [-8,1 [uu [5, +oo [#

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