Solving Linear Equations | 求解线性方程

📚 Solving Linear Equations | 求解线性方程

Linear equations are a cornerstone of Key Stage 3 mathematics. In the Cambridge Checkpoint syllabus, you first encounter them around page 59, where you start building the skills to find unknown values. Understanding how to solve equations will help you in algebra, geometry, and even science.

线性方程是 KS3 数学的基石。在剑桥 Checkpoint 大纲中，大约在第 59 页你会首次遇到它们，并开始学习如何求解未知数。理解如何解方程不仅对代数有帮助，对几何甚至科学也很有用。

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

A linear equation is a mathematical statement that shows two expressions are equal, and it contains one or more variables raised only to the power of 1. For example, x + 3 = 7 and 2x = 10 are linear equations. The goal is to find the value of the unknown (often x) that makes the equation true.

线性方程是表明两个表达式相等的数学陈述，其中变量的指数仅为 1。例如，x + 3 = 7 和 2x = 10 都是线性方程。我们的目标是找到使方程成立的未知数（通常用 x 表示）的值。

Key features: no variables in the denominator, no x² or higher powers, and only one unknown in most early problems.

关键特征：分母中不含变量，没有 x² 或更高次幂，并且在早期问题中通常只有一个未知数。

2. Balancing the Equation | 平衡方程

Think of an equation as a perfectly balanced scale. Whatever operation you do to one side, you must do exactly the same to the other side to keep the balance. This is the golden rule of solving equations.

将方程想象成一个完全平衡的天平。无论你对一边进行什么运算，都必须对另一边进行完全相同的运算以保持平衡。这是解方程的金科玉律。

If we have x + 5 = 12, we can subtract 5 from both sides to isolate x. The scale stays balanced: x + 5 − 5 = 12 − 5, so x = 7.

如果我们有 x + 5 = 12，我们可以从两边减去 5 来分离 x。天平保持平衡：x + 5 − 5 = 12 − 5，因此 x = 7。

x + 5 = 12 → subtract 5 from both sides → x = 7

x + 5 = 12 → 两边减 5 → x = 7

3. Solving One-Step Equations Using Addition or Subtraction | 用加减法求解一步方程

When a constant is added to or subtracted from the variable, use the inverse operation

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