Inequalities for AQA A-Level Maths | A-Level AQA 数学不等式考点精讲

📚 Inequalities for AQA A-Level Maths | A-Level AQA 数学不等式考点精讲

Inequalities form a core part of AQA A-Level Mathematics, appearing across pure algebra, graphical methods, and even applied contexts. A solid grasp of techniques – from linear to rational, from absolute values to discriminants – will give you the confidence to tackle any exam question. This guide covers all essential types with clear examples and practical advice.

不等式是 AQA A-Level 数学的核心组成部分，出现在纯代数、图形解法甚至应用背景中。牢固掌握求解技巧——从线性到有理不等式，从绝对值到判别式——将使你能够自信地应对任何考试题目。本指南涵盖所有基本类型，并配以清晰的示例和实用建议。

1. Solving Linear Inequalities | 解线性不等式

Linear inequalities are solved much like linear equations, but with one golden rule: if you multiply or divide both sides by a negative number, you must reverse the inequality sign.

线性不等式的解法与线性方程很相似，但有一条黄金法则：如果两边乘以或除以一个负数，必须反转不等号。

Example 1: Solve 3x – 7 < 5. Add 7 to both sides: 3x < 12. Divide by 3 (positive, no sign change): x < 4.

示例 1：解 3x – 7 < 5。两边加 7：3x < 12。除以 3（正数，不等号不变）：x < 4。

Example 2: Solve 5 – 2x ≥ 11. Subtract 5: -2x ≥ 6. Divide by -2 (negative, reverse sign): x ≤ -3.

示例 2：解

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