Cambridge KS3 Maths: Solving Linear Equations | 剑桥KS3数学：解一元一次方程

📚 Cambridge KS3 Maths: Solving Linear Equations | 剑桥KS3数学：解一元一次方程

This revision guide supports worksheet p42_2.pdf and focuses on solving linear equations, a core skill in the Cambridge Lower Secondary Mathematics curriculum. You will learn how to keep equations balanced, undo operations in the correct order, and check your solutions.

本复习指南配套练习 p42_2.pdf，重点讲解解一元一次方程，这是剑桥初中数学课程的核心技能。你将学习如何保持等式平衡、按正确顺序逆运算以及检验解。

1. What Is a Linear Equation? | 什么是一元一次方程？

A linear equation is an equation in which the unknown appears only to the first power. It has no squares, cubes, or unknown variables in denominators.

线性方程是未知数只出现一次方的方程。它没有平方、立方，也没有未知数出现在分母中。

Linear equations can usually be written as ax + b = c or ax + b = cx + d, where a, b, c and d are numbers. They are called ‘linear’ because their graphs are straight lines.

线性方程通常可以写成 ax + b = c 或 ax + b = cx + d 的形式，其中 a、b、c、d 是数字。它们被称为“线性”是因为它们的图像是直线。

Examples include x + 5 = 12, 2x − 3 = 9, and 4(x − 1) = 12.

例子包括 x + 5 = 12、2x − 3 = 9 和 4(x − 1) = 12。

2. The Balance Method | 天平法

The balance method is the key idea behind solving any equation. Think of an equation as a balanced set of scales: the left side must equal the right side.

天平法是解任何方程的关键思想。把方程想象成一架平衡的天平：左边必须等于右边。

• Add or subtract the same amount from both sides — 在两边加上或减去相同的量。
• Multiply or divide both sides by the same non-zero amount — 将两边同时乘以或除以相同的非零量。

As long as you do the same operation to both sides, the equation stays balanced. This allows you to isolate the unknown step by step.

只要你对两边执行相同的运算，方程就会保持平衡。这使你能够一步一步地分离未知数。

3. Solving One-Step Equations | 解一步方程

A one-step equation needs only one inverse operation to solve it. Undo addition with subtraction, subtraction with addition, multiplication with division, and division with multiplication.

一步方程只需一次逆运算即可求解。用减法抵消加法，用加法抵消减法，用除法抵消乘法，用乘法抵消除法。

Example 1: Solve x + 7 = 15.

例1：解方程 x + 7 = 15。

x + 7 − 7 = 15 − 7 → x = 8

Example 2: Solve 5x = 35.

例2：解方程 5x = 35。

5x ÷ 5 = 35 ÷ 5 → x = 7

Example 3: Solve x ÷ 6 = 4.

例3：解方程 x ÷ 6 = 4。

更多咨询请联系16621398022（同微信）