Answer: Between the two parallel boundary lines, in the first quadrant.
- A Mostly outside both boundary lines, away from the bounded strip
- B Between the two parallel boundary lines, in the first quadrant
- C Just on the line x + y = 4, treating it as an equality constraint alone
- D Just on the line x + y = 8, treating it as an equality constraint alone
Correct answer: B. Between the two parallel boundary lines, in the first quadrant
Explanation: The region satisfying both x+y>=4 and x+y<=8 in the first quadrant is the band between the two parallel lines x+y=4 and x+y=8.
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.