Question

How do you solve `1/3abs(1/2x-2) >= 2`?

Answer 1

`(-oo,-8]uu[16,oo)`

Explanation:

`"inequalities of the type "|x|>=a`

`"always have solutions of the form"`

`x<= -a" or "x>=a`

`"isolate "|1/2x-2|" by dividing both sides by "1/3`

`rArr|1/2-2|>=6`

`rArr1/2x-2<=-6" or "1/2x-2>=6`

`"add 2 to both sides of both inequalities"`

`rArr1/2x<=-4" or "1/2x>=8`

`"multiply both sides of both inequalities by 2"`

`rArrx <=-8" or "x>=16`

`x in(-oo,-8]uu[16,oo)larrcolor(blue)"in interval notation"`