Cambridge KS3 Mathematics: Solving Linear Equations Step by Step | 剑桥 KS3 数学：逐步解线性方程

📚 Cambridge KS3 Mathematics: Solving Linear Equations Step by Step | 剑桥 KS3 数学：逐步解线性方程

Linear equations are one of the most important topics in the Cambridge KS3 mathematics curriculum. They appear in number, algebra and problem-solving questions, and they provide the foundation for more advanced work in graphs, sequences and formulae. In this article, you will learn how to solve linear equations step by step, avoid common errors and apply your skills to word problems.

线性方程是剑桥 KS3 数学课程中最重要的主题之一。它们出现在数、代数与问题解决题中，并且为图像、数列和公式等更高级的内容打下基础。在本文中，你将逐步学习如何解线性方程、避免常见错误，并把技能应用到文字题中。

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

le, such as x, and it can be written in the form ax + b = c, where a, b and c are numbers.

线性方程是指未知数只出现一次幂的方程。它通常包含一个变量，例如 x，并且可以写成 ax + b = c 的形式，其中 a、b 和 c 是数。

6 are all linear equations. The variable is not squared, cubed or placed in a denominator.

例如，3x + 2 = 14、5y − 7 = 18 和 x/4 + 1 = 6 都是线性方程。变量没有被平方、立方，也没有出现在分母中。

The main goal is to find the value of the unknown that makes the equation true. This value is called the solution or root.

主要目标是求出使等式成立的未知数的值。这个值称为方程的解或根。

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2. Key Vocabulary | 关键术语

Before you start solving, make sure you understand these key words. Knowing the correct vocabulary will help you follow each step and explain your method clearly in class.

在开始解题之前，请确保你理解以下关键词。掌握正确的术语将帮助你跟上每一个步骤，并在课堂上清晰地解释你的方法。

Term	Definition	中文定义
Equation	A statement that two expressions are equal, using the = sign.	用等号表示两个表达式相等的陈述。
Unknown or variable	The letter that stands for the missing number.	代表缺失数字的字母。
Coefficient	The number in front of a variable, such as 3 in 3x.	变量前面的数，例如 3x 中的 3。
Constant	A number on its own that does not change.	单独出现且不发生变化的数。
Balance	The idea that both sides of an equation must stay equal.	等式两边必须保持相等的思想。

Understanding these terms will help you follow each step without confusion and answer short-answer questions accurately.

理解这些术语将帮助你清晰地跟上每一个步骤，并准确回答简答题。

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3. The Balancing Method | 天平法（等式平衡法）

An equation is like a balance scale. Whatever you do to one side, you must do to the other side. This is the golden rule of solving equations.

方程就像一架天平。你对一边所做的任何操作，都必须对另一边做同样的操作。这是解方程的黄金法则。

If you add, subtract, multiply or divide one side by a number, you must do exactly the same to the other side to keep the equation balanced. Think of the two pans of a scale staying level.

如果你对一边加、减、乘或除以一个数，你必须对另一边做完全相同的操作，以保持等式平衡。想象天平的两个托盘始终保持水平。

x + 3 = 10 → x + 3 − 3 = 10 − 3 → x = 7

This method allows you to isolate the unknown on one side of the equation. Always write the operation you are performing on both sides on the same line.

这种方法可以让你把未知数单独分离到等式的一边。请始终在同一行中写出你对两边所执行的运算。

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4. Solving One-Step Equations | 解一步方程

One-step equations require only one operation to isolate the variable. For addition or subtraction equations, use the inverse operation.

一步方程只需要一步运算即可分离变量。对于加法或减法方程，使用逆运算即可。

Example 1: Solve x + 9 = 20.

例 1：解方程 x + 9 = 20。

x + 9 − 9 = 20 − 9 → x = 11

Example 2: Solve y − 5 = 12.

例 2：解方程 y − 5 = 12。

y − 5 + 5 = 12 + 5 → y = 17

For multiplication or division equations, divide or multiply both sides by the same non-zero number.

对于乘法或除法方程，两边同时除以或乘以同一个非零数。

Example 3: Solve 4x = 28.

例 3：解方程 4x = 28。

4x ÷ 4 = 28 ÷ 4 → x = 7

Example 4: Solve x/5 = 3.

例 4：解方程 x/5 = 3。

x/5 × 5 = 3 × 5 → x = 15

g it back into the original equation. For Example 3, 4 × 7 = 28, so the answer is correct.

始终通过将答案代回原方程来检验。例如例 3 中，4 × 7 = 28，因此答案正确。

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5. Solving Two-Step Equations | 解两步方程

Two-step equations involve two operations, such as multiplication and addition. To solve them, undo the operations in the reverse order: first the constant, then the coefficient.

两步方程涉及两种运算，例如乘法和加法。解这类方程时，按相反顺序逆运算：先处理常数，再处理系数。

Example 1: Solve 3x + 2 = 14.

例 1：解方程 3x + 2 = 14。

3x + 2 − 2 = 14 − 2 → 3x = 12

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