Cambridge KS3 Maths: Linear Equations Practice (p259_2) | 剑桥 KS3 数学：一元一次方程练习（p259_2）

📚 Cambridge KS3 Maths: Linear Equations Practice (p259_2) | 剑桥 KS3 数学：一元一次方程练习（p259_2）

Welcome to this Cambridge KS3 Mathematics revision article based on Practice Sheet p259_2. The focus is linear equations, one of the most important algebraic skills at Key Stage 3. We will cover balancing, two-step equations, brackets, fractions, checking, word problems and common errors. Work through each section slowly and attempt the practice questions yourself.

欢迎阅读这篇基于练习卷 p259_2 的剑桥 KS3 数学复习文章。重点是一元一次方程，这是 Key Stage 3 代数中最重要的技能之一。我们将学习天平法、两步方程、去括号、分数系数、检验解、文字题和常见错误。请慢慢完成每个部分，并自己尝试练习题。

1. Understanding Linear Equations | 理解一元一次方程

A linear equation is an equation in which the unknown, often written as x, appears only to the power of 1. The equation forms a straight line when graphed. At KS3, most equations have one unknown and one solution.

一元一次方程是未知数（通常写作 x）只出现一次幂的方程。它在图像上形成一条直线。在 KS3 阶段，大多数方程只有一个未知数和一个解。

Examples include x + 5 = 12, 3y − 2 = 16 and 4(n + 1) = 28. The goal is to find the value of the unknown that makes the equation true.

例如 x + 5 = 12、3y − 2 = 16 和 4(n + 1) = 28。目标是求出使方程成立的未知数的值。

x + 5 = 12 and 3y − 2 = 16

2. Balancing Method | 天平法

Think of an equation as a balance. Whatever you do to one side, you must do to the other side. This keeps the equation true.

把方程想像成一座天平。你对一边做的任何操作，也必须对另一边做，这样方程才能保持成立。

To solve x + 7 = 15, subtract 7 from both sides: x + 7 − 7 = 15 − 7, so x = 8.

要解 x + 7 = 15，两边同时减去 7：x + 7 − 7 = 15 − 7，因此 x = 8。

x + 7 = 15 → x = 15 − 7 → x = 8

Always use inverse operations: addition is undone by subtraction, multiplication by division, and vice versa.

总是使用逆运算：加法由减法抵消，乘法由除法抵消，反之亦然。

3. Solving Two-Step Equations | 解两步方程

A two-step equation has two operations attached to the unknown. For example, in 2x + 3 = 11, the unknown x is first multiplied by 2 and then 3 is added.

两步方程中有两个运算作用在未知数上。例如，在 2x + 3 = 11 中，未知数 x 先乘以 2，然后加 3。

Undo the addition or subtraction first, then undo the multiplication or division. This order is the reverse of the order of operations, sometimes called BIDMAS or BODMAS.

先消去加法或减法，再消去乘法或除法。这个顺序与运算顺序（有时称为 BIDMAS 或 BODMAS）相反。

2x + 3 = 11 → 2x = 8 → x = 4

4. Equations with Brackets | 带括号的方程

When an equation contains brackets, expand them first using the distributive law. Multiply the term outside by each term inside the brackets.

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