Solving Two-Step Linear Equations | 解两步线性方程

📚 Solving Two-Step Linear Equations | 解两步线性方程

In Cambridge KS3 mathematics, solving equations is a core algebra skill. A two-step linear equation involves exactly two inverse operations. This article breaks the process into clear steps, with worked examples, common errors and practice questions.

在剑桥 KS3 数学中，解方程是代数核心技能。两步线性方程恰好包含两次逆运算。本文将解题过程拆分为清晰步骤，并提供例题、常见错误和练习题。

1. What Is a Two-Step Equation? | 什么是两步方程？

In KS3 algebra, a linear equation is an equation where the unknown is not raised to any power higher than 1. A two-step equation has the general form ax + b = c, where a and b are numbers and x is the unknown. This means you must carry out exactly two inverse operations to solve it. For example, 3x + 4 = 19 is a two-step equation because x is first multiplied by 3, then 4 is added.

在 KS3 代数中，线性方程是指未知数的次数不超过 1 的方程。两步方程的一般形式为 ax + b = c，其中 a 和 b 是数字，x 是未知数。这意味着你必须恰好进行两次逆运算才能解出它。例如，3x + 4 = 19 就是一个两步方程，因为 x 先乘以 3，再加 4。

The word ‘two-step’ does not mean the solution is difficult. It simply tells you that two operations have been applied to the unknown, so you need to reverse two operations in the correct order.

‘两步’ 这个词并不意味着解题很难。它只是告诉你未知数经历了两次运算，因此你需要按正确顺序反推两次运算。

ax + b = c

2. Understanding the Balance Rule | 理解天平法则

All equation solving in KS3 depends on the balance rule. Think of each side of the equation as a pan on an old-fashioned balance scale. If you add, subtract, multiply or divide one side by a number, you must do exactly the same to the other side. This keeps the equation true while changing its form.

KS3 中所有解方程都依赖于天平法则。把方程的两边想象成老式天平的两个托盘。如果你对一边加、减、乘或除以一个数，必须对另一边做完全相同的操作。这样可以在保持方程成立的同时改变方程的形式。

For example, if 3x + 4 = 19, you can subtract 4 from both sides because 4 is being added on the left. The equation remains balanced.

例如，如果 3x + 4 = 19，你可以两边同时减去 4，因为左边加上了 4。方程保持平衡。

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