Solving Linear Equations (Cambridge KS3, p187, Exercise 2) | 解一元一次方程（剑桥 KS3，第 187 页练习 2）

📚 Solving Linear Equations (Cambridge KS3, p187, Exercise 2) | 解一元一次方程（剑桥 KS3，第 187 页练习 2）

Linear equations are one of the most important tools in KS3 mathematics. They appear in algebra, geometry, and real-life problem solving. This article reviews the key skills needed to solve linear equations, using the p187_2 exercise as a starting point. You will learn how to isolate the unknown, handle brackets and fractions, and check your work.

线性方程是 KS3 数学中最重要的工具之一。它们出现在代数、几何和实际问题中。本文以 p187_2 练习为起点，复习解一元一次方程所需的关键技能。你将学会如何分离未知数、处理括号和分数，以及检查你的解答。

1. What is a linear equation? | 什么是线性方程？

A linear equation is an algebraic statement in which the unknown variable appears only to the first power. For example, 4x + 1 = 9 and 2y – 3 = y + 5 are both linear equations. There are no x² terms, no square roots, and no variables in the denominator.

线性方程是一个代数等式，其中未知变量只以一次幂出现。例如，4x + 1 = 9 和 2y – 3 = y + 5 都是线性方程。其中没有 x² 项，没有平方根，也没有变量出现在分母中。

The solution of a linear equation is the value of the variable that makes the statement true. In 4x + 1 = 9, the solution is x = 2 because 4(2) + 1 = 9. Solving means finding every value that satisfies the equation.

线性方程的解是使等式成立的变量值。在 4x + 1 = 9 中，解是 x = 2，因为 4(2) + 1 = 9。解方程意味着找到所有使等式成立的值。

On a graph, a linear equation in two variables always produces a straight line. That is why it is called ‘linear’. In KS3, most linear equations you solve have one unknown, such as x or y.

在图上，含有两个变量的线性方程总是形成一条直线。这就是它被称为“线性”的原因。在 KS3 中，你遇到的大多数线性方程只有一个未知数，例如 x 或 y。

2. Using inverse operations | 使用逆运算

To solve a linear equation, rearrange it so that the variable is alone on one side. This is done by applying inverse operations to both sides. Addition and subtraction undo each other; multiplication and division undo each other.

解线性方程时，要重新整理方程，使变量单独位于等号一边。通过对方程

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