📚 Solving Linear Equations with Fractions and Brackets | 解含分数和括号的线性方程
Welcome to this Cambridge KS3 Mathematics revision guide. Linear equations are one of the most important algebra topics at Key Stage 3. In this article, we focus on solving equations that involve brackets and fractions, which often appear in end-of-topic tests and school examinations. Mastering these skills will build a strong foundation for IGCSE and beyond.
欢迎阅读本篇剑桥 KS3 数学复习指南。线性方程是第三学段代数最重要的主题之一。本文将重点讲解含有括号和分数的方程求解，这类题目经常出现在单元测验和学校考试中。掌握这些技能将为 IGCSE 及更高阶段的学习打下坚实基础。
1. What Is a Linear Equation? | 什么是线性方程？
and c are numbers and x is the variable. Linear equations describe a straight line when plotted on a graph.
线性方程是指未知数的指数为 1 的代数等式。它通常可以写成 ax + b = c 的形式，其中 a、b、c 是数字，x 是未知数。线性方程在坐标图上描绘出来是一条直线。
1)/3 = 5. Nonlinear equations such as x² + 2 = 6 or 1/x = 3 are not covered in this topic.
线性方程的例子包括 3x + 5 = 14、4(x − 2) = 2x + 6 以及 (2x + 1)/3 = 5。非线性的方程如 x² + 2 = 6 或 1/x = 3 不在本主题范围内。
2. Key Vocabulary | 关键术语
Before solving equations, you need to be confident with the language of algebra. The variable is the letter that represents an unknown number, often x. A coefficient is the number multiplying the variable, such as 3 in 3x. A constant is a number on its own, such as 5.
在解方程之前，你需要熟悉代数语言。变量是表示未知数的字母，通常用 x。系数是乘以变量的数字，例如 3x 中的 3。常数是单独出现的数字，例如 5。
and RHS (right-hand side). For example, in 2x + 3 = 7, the LHS is 2x + 3 and the RHS is 7.
其他重要术语包括表达式、方程、项、同类项、逆运算、左边 LHS 和右边 RHS。例如，在 2x + 3 = 7 中，左边是 2x + 3，右边是 7。
3. Simplifying Expressions Before Solving | 解方程前的代数式化简
Many equations contain like terms that should be collected first. Like terms have exactly the same variable part, such as 2x and 5x, or 3 and −7. You can combine them by adding or subtracting their coefficients.
许多方程含有需要先合并的同类项。同类项具有完全相同的字母部分，例如 2x 和 5x，或 3 和 −7。你可以通过加减它们的系数来合并同类项。
x + 7. If the equation is 4x + 2 − x + 5 = 16, then it becomes 3x + 7 = 16 before solving.
例如，化简 4x + 2 − x + 5 得到 3x + 7。如果方程为 4x + 2 − x + 5 = 16，那么先化简为 3x + 7 = 16，然后再求解。
4. Expanding Brackets | 展开括号
must multiply the term outside the bracket by every term inside the bracket. Be careful with signs when the number outside is negative.
展开括号就是使用分配律：a(b + c)
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