Solving Linear Equations (Cambridge KS3, p260_1) | 解一元一次方程（剑桥 KS3，p260_1）

📚 Solving Linear Equations (Cambridge KS3, p260_1) | 解一元一次方程（剑桥 KS3，p260_1）

Linear equations are the building blocks of algebra in the Cambridge KS3 mathematics curriculum. Whether you are working through a worksheet labelled p260_1 or a textbook exercise, the methods in this article apply directly. We will work through one-step, two-step, and equations with brackets or variables on both sides.

一元一次方程是剑桥 KS3 数学课程中代数的基础内容。无论你正在完成 p260_1 练习页还是课本习题，本文的方法都直接适用。我们将一起学习一步方程、两步方程，以及含括号或两边都有变量的方程。

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

A linear equation is an equation in which the variable appears only to the power of 1 and is not multiplied or divided by another variable. Its graph is always a straight line, which is why it is called ‘linear’. For example, 2x + 3 = 11 and x − 4 = 9 are linear equations.

一元一次方程是指变量只出现一次方、且不与其他变量相乘或相除的方程。它的图像总是一条直线，因此被称为线性方程。例如 2x + 3 = 11 和 x − 4 = 9 都是一元一次方程。

In KS3, you will meet equations that involve one unknown, usually written as x. The goal is to find the value of x that makes the equation true. This value is called the solution or root of the equation.

在 KS3 阶段，你会遇到只含一个未知数（通常写作 x）的方程。目标就是求出使方程成立的 x 值，这个值叫做方程的解或根。

2. The Balance Method | 天平法

The balance method is the most reliable way to solve linear equations. Think of an equation as a set of balance scales: the left-hand side must always equal the right-hand side. Whatever operation you do to one side, you must also do to the other side to keep the equation balanced.

天平法是解一元一次方程最可靠的方法。把方程想象成一台天平：左边必须始终等于右边。无论你对一边做什么运算，另一边也必须做同样的运算，才能保持方程平衡。

For example, to solve x + 5 = 12, subtract 5 from both sides. This keeps the scales balanced and isolates x on one side. The same idea applies to addition, subtraction, multiplication, and division.

例如，解方程 x + 5 = 12 时，两边同时减去 5。这样天平保持平衡，x 就在一边被单独分离出来。同样的思路也适用于加、减、乘、除。

3. Solving One-Step Equations | 解一步方程

One-step equations require just one inverse operation to find the unknown. The inverse of addition is subtraction, the inverse of subtraction is addition, the inverse of multiplication is division, and the inverse of division is multiplication.

一步方程只需要进行一次逆运算就能求出未知数。加法的逆运算是减法，减法的逆运算是加法，乘法的逆运算是除法，除法的逆运算是乘法。

• If x + 6 = 15, subtract 6 from both sides: x = 9.
• If x − 7 = 20, add 7 to both sides: x = 27.
• If 4x = 32, divide both sides by 4: x = 8.
• If x ÷ 5 = 9, multiply both sides by 5: x = 45.

对应中文：若 x + 6 = 15，两边减 6 得 x = 9；若 x − 7 = 20，两边加 7 得 x = 27；若 4x = 32，两边除以 4 得 x = 8；若 x ÷ 5 = 9，两边乘以 5 得 x = 45。

Always write each step on a new line and keep the equals signs lined up. This makes your working clear and helps you spot mistakes.

每一步都另起一行书写，并将等号对齐。这样解题过程清晰，也便于发现错误。

4. Solving Two-Step Equations | 解两步方程

Two-step equations involve two operations, such as multiplication and addition. To solve them, reverse the order of operations: undo addition or subtraction first, then undo multiplication or division.

两步方程含有两个运算，例如乘法和加法。解这类方程时要逆着运算顺序来：先消去加减法，再消去乘除法。

For example, solve 2x + 3 = 11. First subtract 3 from both sides to get 2x = 8. Then divide both sides by 2 to get x = 4.

例如，解方程 2x + 3 = 11。先两边同时减去 3，得到 2x = 8。然后两边同时除以 2，得到 x = 4。

2x + 3 = 11 → 2x = 8 → x = 4

Here is another example: solve 5x − 4 =

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