Question

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

Answer 1

`|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)`.