Regions Defined by Inequalities | 不等式定义的区域

📚 Regions Defined by Inequalities | 不等式定义的区域

In Edexcel A Level Mathematics, a ‘region’ is a set of points in the coordinate plane that satisfy one or more inequalities. Unlike an equation, which gives a line or curve, an inequality selects one side of that line or curve. This topic often appears in Pure Year 1 and supports later linear programming problems.

在爱德思 A Level 数学中，”区域” 是坐标平面内满足一个或多个不等式的点集。方程给出的是直线或曲线，而不等式则选取直线或曲线的某一侧。这一主题常出现在 Pure Year 1 中，并为后续的线性规划问题奠定基础。

1. What Is a Region? | 什么是区域

A region is the set of all points (x, y) whose coordinates make an inequality true. For example, the inequality x + y < 4 does not describe only the line x + y = 4; it describes all points on one side of that line.

区域是所有满足某个不等式的点 (x, y) 的集合。例如，不等式 x + y < 4 描述的不是直线 x + y = 4 本身，而是这条直线某一侧的所有点。

To represent a region, you first draw the boundary line x + y = 4, then decide which side of the line satisfies the inequality. The boundary may be included or excluded depending on the inequality symbol.

为了表示区域，首先画出边界线 x + y = 4，然后判断直线的哪一侧满足不等式。根据不等号的不同，边界线可能包含在区域内，也可能不包含。

2. Boundary Lines: Solid vs Dashed | 边界线：实线与虚线

If the inequality uses ≤ or ≥, the boundary line is included in the region and is drawn as a solid line. If the inequality uses < or >, the boundary line is not included and is drawn as a dashed line.

如果不等式使用 ≤ 或 ≥，边界线包含在区域内，应画成实线。如果不等式使用 < 或 >，边界线不包含在区域内，应画成虚线。