Draw intervals on the same number line and retain only the overlap. The endpoint is included only if all required conditions include it.
Example
Solve x2≤9 and x>1. The first gives [−3,3], the second (1,∞). Their intersection is (1,3]. For x+3/(x−2), combine x≥−3 with x=2: the domain is [−3,2)∪(2,∞).
Avoid this mistake
Adding solution intervals together by union solves an “or” question, not an “and” question. Some intersections are empty.
Mr. Integral