📚 Linear Equations and Inequalities: Series 400 | 线性方程与不等式：系列 400
Linear equations and inequalities are the foundation of algebra at IGCSE level. This revision guide walks through the balancing method, equations with brackets, fractions, variables on both sides, and the key rules for solving and representing inequalities. Work through each section carefully and practise the examples before attempting exam-style questions.
线性方程与不等式是 IGCSE 阶段代数的基础。本复习指南将系统讲解平衡法、含括号、含分数、变量在两边等方程，以及求解和表示不等式的关键规则。请仔细学习每一节，并在尝试考试题型前练习相关例题。
1. What is a Linear Equation? | 什么是线性方程？
here a, b and c are numbers. For example, x + 5 = 12 and 4x − 7 = 13 are linear equations.
线性方程是指未知数的最高次数为 1 的方程。它通常可以写成 ax + b = c 的形式，其中 a、b、c 是常数。例如 x + 5 = 12 和 4x − 7 = 13 都是线性方程。
The word 'linear' u are expected to solve linear equations using algebraic manipulation rather than guesswork.
“线性”一词来源于 y = ax + b 的图像是一条直线。在 IGCSE 考试中，你需要用代数变形来解线性方程，而不是靠猜测。
able that makes both sides equal. For example, x = 7 solves x + 5 = 12 because 7 + 5 = 12.
方程的解是使等式两边相等的未知数的值。例如 x = 7 是 x + 5 = 12 的解，因为 7 + 5 = 12。
2. Balancing Method: The Golden Rule | 平衡法：黄金法则
The balancing method means that whatever you do to one side of an equation, you must also do to the other side. This keeps the equation balanced, just like a pair of scales.
平衡法是指对方程一边进行任何运算，另一边也必须进行相同运算。这样方程才能保持平衡，就像天平一样。
The main operations are: add or subtract the same number from both sides; multiply or divide both sides by the same non-zero number. These operations do not change the solution.
主要运算有：两边同时加上或减去同一个数；两边同时乘以或除以同一个非零数。这些运算不会改变方程的解。
x + 3 = 10 → x + 3 − 3 = 10 − 3 → x = 7
The aim is to isolate the variable on one side of the equation. Always perform inverse operations step by step and write each line neatly.
目标是把未知数单独留在方程的一边。始终按逆运算一步一步操作，并把每一步写清楚。
3. Solving Two-Step Equations | 解两步方程
A two
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