Answer: k >= 4.
- A k >= 4
- B k <= 4
- C k >= 2
- D k <= 2
Correct answer: A. k >= 4
Explanation: At (3,1): x+y=4 and x-y=2. For (3,1) to be feasible under x+y<=k, we need k >= 4 (the second constraint x-y<=2 is already satisfied with equality).
One-variable inequalities use open (excluded) or closed (included) circles on a number line; two-variable inequalities use a dashed (strict) or solid (non-strict) boundary line, with the solution being the entire shaded half-plane on one side of it.
Concept context
Solving linear inequalities in one and two variables algebraically and graphically, and representing solutions on a number line or as a region in a plane.