📚 Solving Linear Equations | 解一元一次方程
Linear equations are one of the first algebraic tools you meet in KS3 Cambridge Mathematics. They allow you to find unknown values by using balance and inverse operations. This article explains the core ideas step by step, from one-step equations to equations with brackets, fractions, and unknowns on both sides.
一元一次方程是 KS3 剑桥数学中最早接触的代数工具之一。通过平衡法和逆运算，你可以求出未知数的值。本文将一步步讲解核心概念，从一步方程到含括号、分数以及两边都含未知数的方程。
1. What is a Linear Equation? | 什么是一元一次方程？
ear equation because the highest power of x is 1. Linear equations produce a straight line when drawn on a graph, which is why they are called linear.
一元一次方程是指未知数的最高次数为 1 的方程。例如 3x + 5 = 17 就是一个一元一次方程，因为 x 的最高次数是 1。这类方程在图像上表示一条直线，因此被称为线性方程。
An equation has two sides, left and right, separated by an equals sign. The equals sign tells us that both sides have the same value. Solving an equation means finding the value of the unknown that keeps both sides balanced.
方程由等号连接左右两边。等号表示两边数值相等。解方程就是找出使等号保持平衡的未知数的值。
xamples of linear equations are: x + 4 = 9, 2y − 3 = 11, 5(a − 2) = 20, and (m/4) + 1 = 3.
一元一次方程的例子包括：x + 4 = 9、2y − 3 = 11、5(a − 2) = 20 以及 (m/4) + 1 = 3。
Some word problems also lead to linear equations. For example, 'I think of a number, multiply it by 3, add 4, and get 19' can be written as 3n + 4 = 19, where n is the unknown number.
有些文字题也会列出一元一次方程。例如“我想一个数，乘以 3，再加 4，得到 19”可以写成 3n + 4 = 19，其中 n 是未知数。
2. The Balancing Method | 平衡法
The balancing method treats an equation like a set of balance scales. Whatever you do to one side, you must do exactly the same to the other side. This keeps the equation true while you simplify it.
平衡法把方程当作一架天平。你对一边做了什么运算，对另一边也必须做完全相同的运算。这样在化简方程时，等式仍然成立。
For example, if you add 3 to the left side, you must add 3 to the right side. If you divide the left side by 2, you must also divide the right side by 2. This rule is the foundation of all equation solving.
例如，如果你给左边加 3，右边也必须加 3。如果你把左边除以 2，右边也必须除以 2。这一规则是解所有方程的基础。
Add the same number to both sides: x − 5 = 9 → x − 5 + 5 = 9 + 5
两边加同一个数：x − 5 = 9 → x − 5 + 5 = 9 + 5
Subtract the same number from both sides: x + 7 = 12 → x + 7 − 7 = 12 − 7
两边减同一个数：x + 7 = 12 → x + 7 − 7 = 12 − 7
Multiply both sides by the same number: x/3 = 4 → (x/3) × 3 = 4 × 3
两边乘同一个数：x/3 = 4 → (x/3) × 3 = 4 × 3
Divide both sides by the same non-zero number: 4x = 20 → 4x ÷ 4 = 20 ÷ 4
两边除以同一个非零数：4x = 20 → 4x ÷ 4 = 20 ÷ 4
Published by TutorHao | KS3 Mathematics Revision Series | aleveler.com
广告 / Sponsored2026年秋初中实验班提优训练789年级上下册语文数学英语人教苏教北师大译林版 初中七八九教材同步随堂作业本强化习题练…数学 备考教辅 · 正版现货 · 与本文内容相关查看详情 / View on Taobao参考价 ¥19.9更多咨询请联系16621398022（同微信）
备考资讯每日更新，关注不错过考纲变化 · 科目分析 · 学习方法
在微信里长按二维码识别关注
或截图后用「扫一扫 → 相册」选择本图公众号：tutorhao