KS3 Cambridge Mathematics: Mastering Linear Equations | KS3 剑桥数学：掌握一元一次方程

📚 KS3 Cambridge Mathematics: Mastering Linear Equations | KS3 剑桥数学：掌握一元一次方程

Linear equations are one of the most important building blocks of KS3 mathematics. At Cambridge Lower Secondary level, you need to be able to solve equations fluently, use the balancing method, and apply equations to real-world problems. This article will guide you through every key skill and help you avoid common mistakes.

一元一次方程是 KS3 数学中最重要的基础知识之一。在剑桥初中阶段，你需要能够熟练解方程，使用等式平衡法，并运用方程解决实际问题。本文将带你掌握每一项核心技能，并帮助你规避常见错误。

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

A linear equation in one variable is any equation that can be written in the form ax + b = c, where a, b and c are numbers and x is the unknown. The word “linear” means that the variable x only appears to the power 1. There are no x² or x³ terms in this type of equation.

一元一次方程是可以写成 ax + b = c 形式的方程，其中 a、b、c 是数，x 是未知数。“线性”一词表示变量 x 只以一次幂出现。在这类方程中没有 x² 或 x³ 项。

For example, all of the following are linear equations:

例如，以下方程都是一元一次方程：

x + 3 = 7, 2x − 5 = 9, 4(x + 1) = 20, 3x = 15

The solution of an equation is the value of x that makes the equation true. In the first example, x = 4 because 4 + 3 = 7.

方程的解是使等式成立的 x 值。在第一个例子中，x = 4，因为 4 + 3 = 7。

2. The Balancing Method | 等式平衡法

The balancing method is the safest way to solve linear equations. Think of the equation as a balance scale: both sides must stay equal at all times. If you add, subtract, multiply or divide one side, you must do exactly the same to the other side.

等式平衡法是解一元一次方程最稳妥的方法。把方程想象成一个天平：两边必须始终保持相等。如果你对一边进行加、减、乘或除，就必须对另一边做完全相同的运算。

This method helps you isolate x step by step. The key is to use inverse operations. The table below shows the most common inverse pairs.

这个方法能帮助你一步步把 x 分离出来。关键是使用逆运算。下表展示了最常见的逆运算对应关系。

Always write the operation you are doing on both sides. This helps you avoid making mistakes and shows clear working in your exercise book.

每次都要在两边写出你正在进行的运算。这能帮助你避免出错，并且在练习本中展示清晰的解题过程。

3. Solving Simple Equations | 解简单方程

Let us solve x + 5 = 12. To isolate x, subtract 5 from both sides. The equation becomes x + 5 − 5 = 12 − 5, which simplifies to x = 7.

让我们来解 x + 5 = 12。为了分离 x，两边同时减去 5。方程

Published by TutorHao | KS3 Mathematics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）