Page 240 Problem 2: Solving Linear Equations in Geometry | 第240页第2题：几何中的一次方程求解

📚 Page 240 Problem 2: Solving Linear Equations in Geometry | 第240页第2题：几何中的一次方程求解

Many Cambridge KS3 learners meet problems like the one on page 240 where a geometric situation, such as a perimeter or an angle sum, must be expressed as a linear equation and then solved. This article reviews the key skills you need: balancing equations, expanding brackets, clearing fractions, and applying algebra to rectangles and angle facts. Work through each section to build confidence for checkpoint assessments.

许多剑桥 KS3 学生都会遇到第 240 页这类题目：必须把一个几何情境，比如周长或角度和，写成一个一次方程并求解。本文复习你需要的核心技能：平衡方程、展开括号、去分母，以及将代数应用到矩形和角度事实。逐一学习每一节，为 checkpoint 测评建立信心。

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

A linear equation contains an unknown, usually written as x or n, and the unknown is only raised to the power 1. It can be written in forms such as 2x + 3 = 11 or 5(n − 2) = 3n + 4. The word ‘linear’ means the graph of the equation is a straight line.

一次方程含有一个未知数，通常写成 x 或 n，而且未知数的次数只是 1。它可以写成 2x + 3 = 11 或 5(n − 2) = 3n + 4 这样的形式。线性的意思是方程的图像是一条直线。

In KS3 problems, the unknown often represents a length, an angle, a cost, or a score. You do not need to guess the value by trial and improvement; you can use inverse operations to find the exact answer.

在 KS3 题目中，未知数通常表示一个长度、一个角度、一个费用或一个得分。你不需要用试错法猜数值；你可以使用逆运算求出准确答案。

A solution is a value that makes both sides of the equation equal. For example, x = 4 solves 2x + 3 = 11 because 2 × 4 + 3 = 11.

解就是让方程两边相等的值。例如 x = 4 是 2x + 3 = 11 的解，因为 2 × 4 + 3 = 11。

2. The Balance Method | 平衡法

Think of an equation as a balance scale. The left side and right side must stay equal. Whatever operation you do to one side, you must do exactly the same operation to the other side.

把方程想象成一台天平。左边和右边

Published by TutorHao | KS3 Mathematics Revision Series | aleveler.com

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