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How do you solve #abs(x)>=5#?

1 Answer

Sep 3, 2016

#|x|>=5 hArr x in RR-(-5,5)=(-oo,5]uu[5,oo)#.

Explanation:

Recall that, #|y|<,a, (a>0) hArr y in (-a,a)#.

#:. not (|y|<,a, (a>0)) hArr not (y in (-a,a))#.

#:. |y|>=a, (a>0) hArr y !in (-a,a) hArr y in RR-(-a,a), i.e.,#

#y in (-oo,-a]uu[a,oo)#

Clearly, #|x|>=5 hArr x in RR-(-5,5)=(-oo,5]uu[5,oo)#.

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