Question

Which of the following points is a solution of the inequality y < -|x|?

(1, -2)
(1, -1)
(1, 0)

Answer 1

`\large\boxed{(1,\ -2)}`

Explanation:

`|a|=a\ \text{for}\ a\geq0\\\\|a|=-a\ \text{for}\ a<0\\\\\text{Examples}\\\\|3|=3,\ |1.6|=1.6\\|-3|=-(-3)=3,\ |-1.6|=1.6\\===================`

`y<-|x|\\\\\text{Put the values of x and y from the coordinates of the points and check inequality}\\\\(1,\ -2)\to x=1,\ y=-2\\-2<-|1|=-1\qquad\text{CORRECT :)}\\\\(1,\ -1)\to x=1,\ y=-1\\-1<-|1|=-1\qquad\text{FALSE :(}\\\\(1,\ 0)\to x=1,\ y=0\\0<-|1|=-1\qquad\text{FALSE :(}`