Find the set of all z such that neither 2+z nor 2-z is in the interval (-1,1]. Express your answer as an interval or as a union of intervals.

1 answer

If z>=0,
2+z > 1 -- z > -1
2-z <= -1 -- z >= 3

If z<0,
2-z > 1 -- z < 1
2+z <= -1 -- z <= -3

graph those on the number line, and you will find your answer.

Be sure to check a few values to make sure they work, especially at the boundaries.