Graphing a compound inequality of the form x < 2 or x > 5 results in

• A. Two disjoint shaded regions
• B. A single continuous shading between 2 and 5
• C. No shading
• D. Shading on the boundary only

Answer: (A)

Think about what “or” means in a compound inequality: a number must satisfy at least one of the conditions. Here, x < 2 means all numbers to the left of 2 (not including 2), and x > 5 means all numbers to the right of 5 (not including 5). Since a number only has to meet one of these, the solution is everything left of 2 plus everything right of 5. On a number line, that shows up as two separate shaded regions: one to the left of 2 and one to the right of 5, with a gap between 2 and 5. The endpoints 2 and 5 aren’t included because the inequalities are strict. If the inequalities were ≤ or ≥, the endpoints would be included.