Mastering Linear Equations for KS3 Cambridge Maths | 掌握剑桥 KS3 数学一元一次方程

📚 Mastering Linear Equations for KS3 Cambridge Maths | 掌握剑桥 KS3 数学一元一次方程

Linear equations are one of the most important building blocks in the KS3 Cambridge Mathematics course. They appear in topics such as number patterns, functions, geometry problems and word problems. A strong grasp of solving linear equations gives you the tools to handle harder algebra later, including simultaneous equations and quadratic equations.

一元一次方程是剑桥中学数学课程中最重要的基础模块之一。它出现在数列规律、函数、几何问题和实际应用题等多个主题中。扎实掌握一元一次方程的解法，能为你今后学习更难的内容（如联立方程和二次方程）打下坚实基础。

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

A linear equation in one variable is an equation where the unknown, usually written as x, is raised only to the power of 1. This means there are no terms such as x², x³ or 1/x. The graph of a linear equation is always a straight line, which is where the word ‘linear’ comes from.

一元一次方程是指只含有一个未知数（通常用 x 表示），并且未知数的次数仅为 1 的方程。这意味着方程中不会出现 x²、x³ 或 1/x 这样的项。一元一次方程的图像总是直线，所以被称为线性方程。

Ax + B = C

The standard form is Ax + B = C, where A is not zero. For example, 3x + 2 = 11 and x/4 – 5 = 1 are both linear equations.

标准形式为 Ax + B = C，其中 A 不等于零。例如，3x + 2 = 11 和 x/4 – 5 = 1 都是一元一次方程。

When you solve a linear equation, you are finding the value of x that makes the equation true. The solution is the number that balances both sides of the equation exactly.

解一元一次方程，就是找到使等式成立的 x 的值。这个解就是使方程左右两边完全平衡的数。

Exam tip: In Cambridge KS3 tests, you may be asked to identify whether an equation is linear. Always check that the highest power of x is 1.

考试提示：在剑桥 KS3 测试中，可能会要求判断一个方程是否为线性方程。务必检查 x 的最高次数是否为 1。

2. The Balance Method | 天平法

Think of an equation as a balance scale. The left side of the equals sign and the right side must always have the same value. You can only keep the scale balanced if you do the same operation to both sides.

把方程想象成一台天平。等号左右两边必须始终具有相同的值。只有对等式两边同时进行相同的运算，天平才能保持平衡。

This idea is called the balance method. If you add, subtract, multiply or divide one side by a number, you must do exactly the same to the other side.

这种思想称为天平法。如果你

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