Solving Linear Equations | 解一元一次方程

📚 Solving Linear Equations | 解一元一次方程

Linear equations are one of the most fundamental skills in Key Stage 3 mathematics. They appear in almost every topic, from geometry to word problems, and they build the foundation for more advanced algebra at IGCSE and beyond.

一元一次方程是 KS3 阶段数学中最基础的技能之一。它们几乎出现在所有主题中，从几何到应用题，并为 IGCSE 及更高级代数打下基础。

In this article, you will learn how to solve linear equations step by step, check your answers and avoid common errors.

在本文中，你将学习如何逐步解一元一次方程、检验答案并避免常见错误。

---

1. What is a Linear Equation? | 什么是一元一次方程？

re a, b and c are numbers. There are no x² terms, no x³ terms, and no products like x × x.

一元一次方程是指未知数（通常写作 x）的指数仅为 1 的方程。它可以写成 ax + b = c 的形式，其中 a、b、c 是数字。方程中没有 x² 项，没有 x³ 项，也没有像 x × x 这样的乘积。

he highest power of x is 1. The equation x² + 2x = 8 is not linear because it contains x².

例如，3x + 5 = 20 是一个一元一次方程，因为 x 的最高次数是 1。方程 x² + 2x = 8 不是一元一次方程，因为它含有 x²。

---

2. Key Vocabulary | 核心词汇

Key words include variable, coefficient, constant, solution and inverse operation.

关键词包括变量、系数、常数、解和逆运算。

A variable is a letter that stands for an unknown number, often x. A coefficient is the number multiplying the variable, for example 3 in 3x. A constant is a number on its own, such as 5 in x + 5. A solution is the value of the variable that makes the equation true. An inverse operation is the opposite operation, such as addition and subtraction.

变量是表示未知数的字母，通常是 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 x + 5 中的 5。解是使方程成立的变量的值。逆运算是相反的运算，例如加法和减法。

Understanding these words will help you follow the steps more easily.

理解这些词汇将帮助你更容易地跟上解题步骤。

---

3. The Balance Method | 天平法原理

Think of an equation as a balance scale. Whatever you do to one side, you must do to the other side to keep it balanced. This is called the balance method.

把方程想象成一个天平。无论你对一边做什么，你必须对另一边做同样的操作才能保持平衡。这称为天平法。

For example, if you add 3 to the left side, you must add 3 to the right side. If you divide the left side by 2, you must divide the right side by 2.

例如，如果你在左边加 3，你必须在右边也加 3。如果你把左边除以 2，你也必须把右边除以 2。

The balance method ensures that the equality remains true while you isolate the variable.

天平法确保你在隔离变量的同时等号仍然成立。

---

广告 / Sponsored

4. One-Step Equations | 一步方程

A one-step equation needs only one inverse operation to solve. The goal is to get x alone on one side of the equation.

一步方程只需要一次逆运算即可求解。目标是让 x 单独留在方程的一边。

Here is a useful table of operations and their inverse operations.

下面是一个有用的运算与逆运算表。

Operation	Inverse operation
+	−
−	+
×	÷
÷	×

Example: x + 7 = 15. Subtract 7 from both sides: x + 7 − 7 = 15 − 7, so x = 8.

示例：x + 7 = 15。两边同时减去 7：x + 7 − 7 = 15 − 7，因此 x = 8。

x + 7 = 15 → x = 15 − 7 → x = 8

Example: 4x = 28. Divide both sides by 4: 4x ÷ 4 = 28 ÷ 4, so x = 7.

示例：4x = 28。两边同时除以 4：4x ÷ 4 = 28 ÷ 4，因此 x = 7。

4x = 28 → x = 28 ÷ 4 → x = 7

---

5. Two-Step Equations | 两步方程

Two-step equations involve two operations. Always reverse the order of operations: undo addition or subtraction first, then undo multiplication or division.

两步方程包含两种运算。始终逆着运算顺序来做：先消去加法或减法，再消去乘法或除法。

x + 5 = 17. First subtract 5 from both sides: 2x = 12. Then divide both sides by 2: x = 6.

示例：2x + 5 = 17。首先两边减去 5：2x = 12。然后两边除以 2：x = 6。

2x + 5 = 17 → 2x = 12 → x = 6

Example: x/3 − 2

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

更多咨询请联系16621398022（同微信）