Solving Linear Equations: Cambridge KS3 p54_2 | 解一元一次方程：剑桥 KS3 第54页练习2

📚 Solving Linear Equations: Cambridge KS3 p54_2 | 解一元一次方程：剑桥 KS3 第54页练习2

Linear equations are the backbone of algebra at KS3. In this Cambridge KS3 p54_2 style revision guide, you will learn how to solve one-step, two-step, bracket and variable-on-both-sides equations using balance and inverse operations. The unknown, usually written as x, only appears to the power of 1, so every equation can be solved step by step.

一元一次方程是 KS3 代数的基石。在这篇剑桥 KS3 第54页练习2 风格的复习指南中，你将学习如何利用等式平衡和逆运算来解一步、两步、含括号以及两边含未知数的方程。未知数通常写作 x，只出现一次方，因此每一道方程都可以按步骤逐步求解。

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

A linear equation is an equation where the unknown, usually written as x, has degree 1. This means you will only see terms like x, 2x, −3x or x/4, and never x², x³ or 1/x.

一元一次方程是指未知数（通常为 x）的次数为 1 的方程。这意味着你只会看到 x、2x、−3x 或 x/4 这样的项，而不会出现 x²、x³ 或 1/x。

The general form is ax + b = c with a ≠ 0. The solution is the value of x that makes the equation true when substituted back into the original equation.

一般形式为 ax + b = c，其中 a ≠ 0。解就是代入原方程后能使方程成立的 x 值。

ax + b = c, a ≠ 0

2. Balance Principle and Inverse Operations | 等式平衡原理与逆运算

An equation is balanced like a set of scales. If you add, subtract, multiply or divide one side, you must do exactly the same to the other side, otherwise the equation becomes false.

方程像一架平衡的天平。如果你对一边进行加、减、乘、除，就必须对另一边做完全相同的运算，否则方程就不再成立。

The key is to use inverse operations. Addition and subtraction are inverse operations; multiplication and division are inverse operations. Your aim is to isolate x step by step on one side of the equals sign.

关键是使用逆运算。加法与减法互为逆运算；乘法与除法互为逆运算。你的目标是逐步把 x 单独留在等号一边。

The table below shows common inverse pairs you will use when solving equations.

下表展示了你在解方程时常用的逆运算配对。