GCSE CCEA Maths: Inequalities Revision Guide | GCSE CCEA 数学：不等式 考点精讲

📚 GCSE CCEA Maths: Inequalities Revision Guide | GCSE CCEA 数学：不等式 考点精讲

Inequalities are fundamental in GCSE mathematics, forming a core topic in the CCEA specification. They allow you to express a range of possible values rather than a single solution. This guide provides a thorough revision of inequality concepts, from basic linear inequalities to graphical representations and simple quadratics, equipping you with the skills to tackle any exam question confidently.

不等式是GCSE数学的基础内容，是CCEA考试大纲的核心主题。它们让你能够表达一个可能值的范围，而不仅仅是单一的解。本指南彻底复习了不等式的概念，从基础的一元一次不等式到图形表示和简单的二次不等式，帮助你有信心应对任何考试题目。

1. Introduction to Inequalities | 不等式简介

An inequality is a mathematical statement that compares two expressions, indicating that one is larger or smaller than the other. Unlike equations, which state that two things are equal, inequalities define a set of values that satisfy a condition such as ‘greater than’ or ‘less than’. They are used in everyday contexts like speed limits, minimum heights for rides, and budgeting problems.

不等式是比较两个表达式的数学语句，表明一个比另一个大或小。与方程（表明两事物相等）不同，不等式定义了满足“大于”或“小于”等条件的值的集合。它们常用于日常情境，如速度限制、乘坐游乐设施的最低身高以及预算问题。

Understanding inequalities is crucial because they form the basis for more advanced topics in algebra and graphical analysis. In CCEA examinations, you will be asked to solve inequalities, represent them on number lines and coordinate planes, and interpret solutions in real-life contexts.

理解不等式至关重要，因为它们构成了更高阶代数与图形分析的基础。在CCEA考试中，你会被要求解不等式、在数轴和坐标平面上表示它们，并在现实情境中解释解集。

2. Inequality Symbols and Meanings | 不等号及其含义

The four main inequality symbols are: < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to). Additionally, ≠ means ‘not equal to’. It is essential to read these symbols correctly: for instance, x > 5 reads as ‘x is greater than 5’, meaning 5 is not part of the solution. However, x ≥ 5 includes the number 5.

四个主要的不等号是：<（小于）、>（大于）、≤（小于等于）和 ≥（大于等于）。此外，≠ 表示“不等于”。正确阅读这些符号很关键：例如，x > 5 读作“x 大于 5”，意思是 5 不包含在解集中。而 x ≥ 5 则包含数字 5。

The table below summarises the symbols with their meanings and examples:

下表总结了这些符号及其含义和示例：

When working with strict inequalities (< or >), the boundary value is not included; we use an open circle on a number line. With inclusive inequalities (≤ or ≥), the boundary is included, represented by a closed circle. Always read the inequality from the variable side to interpret the range correctly.

处理严格不等式（< 或 >）时，边界值不包含在内；我们在数轴上使用空心圆。对于包含等于的不等式（≤ 或 ≥），边界值包含在内，用实心圆表示。始终从变量那一侧阅读不等式，以正确解释范围。

3. Solving Linear Inequalities | 解一元一次不等式

Solving linear inequalities follows the same logic as solving equations: we isolate the variable by performing inverse operations. The key difference is that the solution is a range of numbers, often expressed with an inequality symbol. You can add, subtract, multiply, or divide both sides, just as you would in an equation, but you must be careful when multiplying or dividing by a negative number (covered in the next section).

解一元一次不等式的逻辑与解方程相同：我们通过逆运算来分离变量。关键区别在于解是一个数字范围，通常用不等号表示。你可以像处理方程一样在两边加、减、乘、除，但必须小心乘以或除以负数的情况（下一节会讲到）。

Example: Solve 4x – 7 > 5. Add 7 to both sides: 4x > 12. Divide both sides by 4: x > 3. The solution states that any number greater than 3 satisfies the inequality. We can check: when x = 4, left side equals 9, which is > 5.

示例：解 4x – 7 > 5。两边加7：4x > 12。两边除以4：x > 3。解集指出任何大于3的数都满足该不等式。我们可以检验：当 x

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