Mathematics

Mathematics

Problem

For the following set of inequalities, identify the correct combination of boundary types (Solid = S, Dashed = D) that must be used while graphing them in the given order. 1. x−y>2x - y > 2 2. y≤5y \le 5 3. 3x+2y≥123x + 2y \ge 12 Which option lists the boundary styles for (1), (2) and (3) respectively? a) S, S, S b) D, S, S c) D, D, D d) D, S, D
Intuitive explanation

When graphing linear inequalities, the boundary line type depends on whether the inequality includes equality: strict inequalities (>> or <<) use dashed lines because points on the boundary don't satisfy the inequality, while non-strict inequalities (≥\ge or ≤\le) use solid lines because boundary points are included in the solution. Just check each inequality's symbol to determine its boundary style.

Intuitive explanation

When graphing linear inequalities, the boundary line type depends on whether the inequality includes equality: strict inequalities (>> or <<) use dashed lines because points on the boundary don't satisfy the inequality, while non-strict inequalities (≥\ge or ≤\le) use solid lines because boundary points are included in the solution. Just check each inequality's symbol to determine its boundary style.

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