📚 Solving Linear Equations | 解一元一次方程
Linear equations are one of the most important building blocks in the Cambridge KS3 mathematics curriculum. They appear in algebra, number problems, geometry and real-life situations. A strong understanding of how to solve them by keeping the equation balanced will help you succeed in Checkpoint tests and later IGCSE work.
一元一次方程是剑桥 KS3 数学课程中最重要的基础模块之一。它们出现在代数、数字问题、几何和实际生活情境中。牢固掌握通过保持等式平衡来解方程的方法，将帮助你在 Checkpoint 考试以及未来的 IGCSE 学习中取得成功。
1. What is a Linear Equation? | 什么是一元一次方程？
A linear equation is an algebraic statement in which two expressions are equal, and the unknown appears only to the first power. In KS3, the unknown is usually written as x, but it can also be a, y, m or any letter. The word 'linear' means that when you draw its graph, you get a straight line.
一元一次方程是两个表达式相等且未知数只出现一次的代数语句。在 KS3 阶段，未知数通常写作 x，但也可以是 a、y、m 或任何字母。“线性”一词表示当你画出它的图像时，得到的是一条直线。
Common examples include:
常见例子包括：
- x + 7 = 15 — one operation
- x + 7 = 15 — 一次运算方程
- 3x − 4 = 11 — two operations
- 3x − 4 = 11 — 两次运算方程
- 2(x + 3) = 14 — brackets
- 2(x + 3) = 14 — 含括号方程
The goal is always to find the value of the unknown that makes the equation true.
目标始终是求出使等式成立的未知数的值。
2. Key Vocabulary and Symbols | 核心词汇与符号
Before solving equations, you need to be confident with the vocabulary. The left-hand side (LHS) is everything to the left of the equals sign, and the right-hand side (RHS) is everything to the right. A solution is the value of the unknown that makes the equation true. A term is a single number, letter or product such as 3x or −5.
在解方程之前，你需要熟悉相关词汇。左边（LHS）是等号左边的所有内容，右边（RHS）是等号右边的所有内容。解就是使等式成立的未知数的值。项是一个单独的数、字母或乘积，如 3x 或 −5。
| Symbol | Meaning | 中文含义 |
|---|---|---|
| = | is equal to | 等于 |
| ≠ | is not equal to | 不等于 |
| < | is less than | 小于 |
| > | is greater than | 大于 |
For equations, the equals sign is the pivot: both sides must have the same value at all times during your working.
对于方程而言，等号是支点：在解题过程中，两边必须始终保持相同的值。
3. The Balancing Method | 天平法
Think of an equation as a balanced scale. If you add, subtract, multiply or divide one side by a number, you must do exactly the same to the other side to keep the scale balanced. This is called the balancing method and it is the foundation of all algebraic solving at KS3.
把方程想象成一个平衡的天平。如果你对一边加上、减去、乘以或除以某个数，你必须对另一边做完全相同的运算，才能保持天平平衡。这称为天平法，是 KS3 阶段所有代数解题的基础。
For example, if x + 5 = 12, you can subtract 5 from both sides:
例如，如果 x + 5
Published by TutorHao | KS3 Mathematics Revision Series | aleveler.com
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