📚 Solving Linear Equations for KS3 | KS3 数学：解一元线性方程
Linear equations are one of the most important building blocks in KS3 mathematics. They appear in algebra, word problems, graphs and even later GCSE work. This article explains how to solve linear equations step by step using the balancing method, with plenty of examples tailored to the Cambridge KS3 syllabus.
线性方程是 KS3 数学中最重要的基础模块之一。它们出现在代数、应用题、图像甚至后续 GCSE 学习中。本文介绍如何用平衡法逐步解一元线性方程，并提供大量贴合剑桥 KS3 大纲的例题。
1. What is a Linear Equation? | 什么是线性方程？
+ 5 = 12 and 3x - 4 = 2x + 7 are both linear equations because x is not squared or cubed.
线性方程是表示两个表达式相等的语句，未知数通常只出现一次方。例如 x + 5 = 12 和 3x - 4 = 2x + 7 都是线性方程，因为 x 没有平方或立方。
The word 'linear' tells us that if we drew the equation as a graph, it would form a straight line. In KS3 we focus on finding the value of the unknown that makes the equation true.
'线性' 一词表示如果把方程画成图像，它会形成一条直线。在 KS3 阶段，我们重点求使方程成立的未知数的值。
2. The Balancing Method | 平衡法
Think of an equation as a set of balance scales. Both sides must always have the same value. Whatever operation we do to one side, we must also do to the other side.
把方程想象成一座天平的左右两盘。两边必须始终保持相等。对一边进行任何运算，另一边也必须进行相同运算。
This idea is the key to all equation solving. If we add, subtract, multiply or divide one side by a number, we must do exactly the same to the other side.
这个思想是解所有方程的关键。如果我们对一边加、减、乘、除一个数，就必须对另一边做完全相同的操作。
| Forward operation | Inverse operation |
| Addition (+) | Subtraction (-) |
| Subtraction (-) | Addition (+) |
| Multiplication (×) | Division (÷) |
| Division (÷) | Multiplication (×) |
The table above shows the inverse operations you will use constantly. Always choose the inverse of the operation that is attached to the unknown.
上表展示了你将反复使用的逆运算。始终选择与未知数相连的运算的逆运算。
3. Solving One-Step Equations | 解一步方程
eded to isolate x. For example, x + 7 = 15 can be solved by subtracting 7 from both sides:
在一步方程中，只需要一步运算就能求出 x。例如 x + 7 = 15，可以两边同时减去 7：
x + 7 - 7 = 15 - 7 → x = 8
Similarly, if the equation is 4x = 36, we divide both sides by 4:
类似地，如果方程是 4x = 36，我们把两边同时除以 4：
4x ÷ 4 = 36 ÷ 4 → x = 9
The operation you choose must be the inverse, or opposite, of the operation attached to x. Addition is undone by subtraction, and multiplication is undone by division.
所选的运算必须是与 x 相连的运算的逆运算，也就是相反运算。加法用减法来抵消，乘法用除法来抵消。
get x = 18. For a subtraction equation like x - 9 = 21, add 9 to both sides to get x = 30.
对于 x ÷ 3 = 6 这样的除法方程，两边同时乘以 3 得到 x = 18。对于 x - 9 = 21 这样的减法方程，两边同时加 9 得到 x = 30。
4. Solving Two-Step Equations | 解两步方程
order of operations. For 2x + 5 = 17, first subtract 5 from both sides, then divide by 2:
两步方程包含两种运算，例如乘法和加法。解这类方程需要逆运算的顺序。对于 2x + 5 = 17，先两边同时减去 5，再两边同时除以 2：
2x + 5 - 5 = 17 - 5 → 2x = 12 → x = 6
Remember: we always undo addition or subtraction before undoing multiplication or division. This is because we normally follow BIDMAS in forward order, so we reverse it when solving.
记住：在解方程时，总是先处理加减，再处理乘除。这是因为我们正向计算时通常遵循 BIDMAS 顺序，解方程时则逆向操作。
= 31. First add 4 to both sides to get 5x = 35, then divide both sides by 5 to get x = 7.
另一个例子是 5x -
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