Sketch the regions which points satisfy `|x+y| ge 2`.

Explanation

`|x+y| ge 2`
`x+y le -2 oe x+y ge 2`
That is,the points lie in the region satisfying the inequality `x+y+ 2 ge 0 or x+y -2 le 0`.
For `x+y +2 le 0`, the points lie on the line `x+y+2=0` or in the half region in which `(0,0)` does not lie as (0, 0) does not satisfy `x+y+ 2 le 0`.
For `x+y-2 ge 0`, the points lie on the (0, 0) does not satisfy `x+y-2 ge 0`.
Hence the required region is as shown in the following figure.