Question

How do you solve `abs(5x-15)-4>=21`?

Answer 1

`(-oo,-2]uu[8,+oo)`

Explanation:

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

`"Always have solutions of the form"`

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

`rArr|5x-15|-4>=21`

`"add 4 to both sides"`

`rArr|5x-15|>=25`

`rArr5x-15<=-25" or "5x-15>=25`

`"add 15 to both sides in both inequalities"`

`rArr5x<=-10" or "5x>=40`

`"divide both sides in both inequalities by 5"`

`rArrx <=-2" or "x>=8larrcolor(blue)"solution"`

`(-oo,-2]uu[8,+oo)larrcolor(blue)"in interval notation"`