📚 Solving Linear Inequalities and Representing Solutions on Number Lines | IGCSE 数学：解一元一次不等式并在数轴上表示解集
Linear inequalities are one of the most practical topics in the IGCSE Mathematics syllabus. They appear in Algebra, Number and Word Problems, and they build directly on the skills you use to solve linear equations. The key difference is that an inequality has a whole range of solutions, so you must describe the solution set clearly on a number line or in interval notation.
一元一次不等式是 IGCSE 数学大纲中最实用的主题之一。它们出现在代数、数与文字题中，并且直接建立在解一元一次方程的技能之上。关键区别在于：不等式具有一整片范围的解，因此你必须清楚地用数轴或区间记号来描述解集。
This revision guide will take you through the symbols, the solving process, the negative-number rule, number line diagrams, interval notation and exam-style word problems. Work through every example and pay close attention to the direction of the inequality sign.
本复习指南将带你掌握不等号、求解过程、负数规则、数轴图、区间记号以及考试型文字题。请认真完成每个例题，并特别注意不等号的方向。
1. Reading Inequality Symbols | 认识不等号
eater than), < (less than), ≥ (greater than or equal to) and ≤ (less than or equal to).
不等式使用四个主要符号之一来比较两个表达式：>（大于）、<（小于）、≥（大于或等于）和 ≤（小于或等于）。
The statement x > 3 means "x is strictly greater than 3", so x = 3 is not allowed. The statement x ≤ 5 means "x is less than or equal to 5", so x = 5 is allowed.
语句 x > 3 表示 "x 严格大于 3"，因此 x = 3 不允许。语句 x ≤ 5 表示 "x 小于或等于 5"，因此 x = 5 是允许的。
You should also recognise the symbol ≠, which means "not equal to". Although it is not usually used for a range, it can appear in inequality statements.
你还应该认识符号 ≠，它表示 "不等于"。虽然它通常不用于表示范围，但可能出现在不等式语句中。
| x > 3 | x is greater than 3 | x 大于 3 |
| x < 3 | x is less than 3 | x 小于 3 |
| x ≥ 3 | x is greater than or equal to 3 | x 大于或等于 3 |
| x ≤ 3 | x is less than or equal to 3 | x 小于或等于 3 |
2. Solving Basic Linear Inequalities | 解基本一元一次不等式
To solve a linear inequality, use the same balancing method as for linear equations: whatever you do to one side, you must do to the other side.
解一元一次不等式时，使用与解一元一次方程相同的平衡方法：对一边进行的每一步操作，另一边也必须进行同样的操作。
For example, x + 3 > 7 can be solved by subtracting 3 from both sides.
例如，x + 3 > 7 可以通过两边同时减去 3 来求解。
x + 3 > 7 → x > 4
Another example is 2x − 5 < 9. Add 5 to both sides, then divide both sides by 2.
另一个例子是 2x − 5 < 9。两边加 5，再两边除以 2。
2x − 5 < 9 → 2x < 14 → x < 7
When the coefficient of x is positive, the inequality sign stays the same. This makes the first few questions straightforward.
当 x 的系数为正时，不等号方向保持不变。这使得前几道题相对简单。
3. Multiplying or Dividing by a Negative Number | 乘以或除以负数时改变不等号方向
The only important difference from equations occurs when you multiply or divide both sides of an inequality by a negative number. You must reverse the direction of the inequality symbol.
与方程唯一重要的区别发生在你用负数乘以或除以不等式两边时。此时你必须改变不等号的方向。
xample, −2x ≤ 6. Dividing both sides by −2 gives x ≥ −3 because the sign must be reversed.
例如，−2x ≤ 6。两边除以 −2 得到 x ≥ −3，因为不等号必须改变方向。
