Solving Linear Equations | 解一元一次方程

📚 Solving Linear Equations | 解一元一次方程

Linear equations are one of the most important building blocks in KS3 mathematics. They appear in algebra, problem-solving and even real-life situations such as working out costs, distances and unknown quantities. This article explains how to solve linear equations step by step, using clear methods and examples suitable for Cambridge KS3 learners.

线性方程是 KS3 数学中最重要的基础内容之一。它出现在代数、问题解决甚至现实生活中，例如计算费用、距离和未知量。本文将逐步解释如何解一元一次方程，使用适合 Cambridge KS3 学生的清晰方法和示例。

1. What Is a Linear Equation? | 什么是线性方程？

A linear equation is an equation in which the unknown variable appears only to the power of 1. For example, x + 3 = 7 and 2x – 5 = 9 are linear equations. The word ‘linear’ comes from the fact that the graph of such an equation is a straight line.

线性方程是指未知变量只出现 1 次方的方程。例如 x + 3 = 7 和 2x – 5 = 9 都是线性方程。’线性’ 一词来源于这类方程的图像是一条直线。

x + 3 = 7, 2x – 5 = 9

An equation such as x² + 2 = 11 is not linear because the variable x has an exponent of 2. Linear equations only contain terms like x, 2x or -5x, never x², x³ or higher powers.

像 x² + 2 = 11 这样的方程不是线性方程，因为变量 x 的指数是 2。线性方程只包含 x、2x 或 -5x 这样的项，绝不超过 x²、x³ 或更高次幂。

2. The Balancing Method | 等式平衡法

To solve a

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