Solving Linear Equations: KS3 Cambridge Maths p36 Worked Example | 解线性方程：剑桥KS3数学第36页例题解析

📚 Solving Linear Equations: KS3 Cambridge Maths p36 Worked Example | 解线性方程：剑桥KS3数学第36页例题解析

Linear equations are a fundamental part of the Cambridge KS3 mathematics curriculum. Being able to solve equations like the one on page 36, question 1, builds the foundation for algebra, problem solving, and later topics such as graphs and inequalities. In this article, we will work through the step-by-step solution of the equation 3(2x – 1) = 4x + 5, check the answer, discuss common mistakes, and explore related problems.

线性方程是剑桥初中数学课程的核心内容。能够解出类似第36页第1题的方程，为代数、问题解决以及后续图像与不等式等课题打下坚实基础。本文将逐步解析方程 3(2x – 1) = 4x + 5，验证答案，讨论常见错误，并探讨相关问题。

1. The Problem | 问题呈现

We are asked to solve the equation 3(2x – 1) = 4x + 5 from page 36, exercise 1. The target is to find the value of x that makes both sides equal.

题目要求解第36页练习1中的方程 3(2x – 1) = 4x + 5。目标是找出使等式两边相等的 x 值。

2. Expanding Brackets | 展开括号

The first step is to expand the bracket on the left-hand side. Multiply 3 by each term inside: 3 × 2x = 6x and 3 × (–1) = –3. This gives 6x – 3. So the equation becomes 6x – 3 = 4x + 5.

第一步是展开左侧的括号。将 3 乘以括号内的每一项：3 × 2x = 6x，3 × (–1) = –3，得到 6x – 3。于是方程变为 6x – 3 = 4x + 5。

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