📚 Solving Linear Inequalities | 解一元一次不等式
Inequalities are everywhere in algebra. Understanding how to solve linear inequalities is a core skill for the Edexcel IGCSE Mathematics exam. This guide breaks down the essential methods, common pitfalls, and exam-style examples so you can solve them with confidence.
不等式在代数中无处不在。掌握一元一次不等式的解法是 Edexcel IGCSE 数学考试的核心能力。本指南将系统讲解基本方法、常见陷阱与考试型例题，帮助你自信地求解不等式。
1. What Are Linear Inequalities? | 什么是线性不等式
A linear inequality is a relationship between two expressions in which the variable is raised to the first power only. For example, 4x – 1 ≤ 15 is a linear inequality. The solution set is the set of all real numbers that make the inequality true. This set often contains infinitely many numbers, so we cannot write it as a single value.
线性不等式是只含一次幂变量与常数组成的比较关系。例如，4x – 1 ≤ 15 就是线性不等式。解集是使不等式成立的所有实数；因为通常包含无限多个数，所以我们不能将其写成一个单一数值。
Here are the symbols you must know:
你需要掌握以下符号：
| Symbol | 符号 | Meaning | 含义 | Example | 示例 |
|---|---|---|
| < | less than | 小于 | x < 3 |
| > | greater than | 大于 | x > 3 |
| ≤ | less than or equal to | 小于或等于 | x ≤ 3 |
| ≥ | greater than or equal to | 大于或等于 | x ≥ 3 |
2. The Number Line Representation | 数轴表示
Unlike an equation such as 3x = 9, which has exactly one solution, an inequality typically has a range of solutions. A number line is a very clear way to show this range. Use an open circle at a value that is not included, and use a closed circle at a value that is included.
与 3x = 9 这类只有一个解的方程不同，不等式通常有一个解集区间。数轴是表示这个区间的非常清晰的方法。遇到不取该点值的用空心圆，遇到取该点值的用实心圆。
For example, x > -2 is shown with an open circle at -2 and an arrow to the right.
例如，x > -2 在数轴上用 -2 处的
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