Solving Linear Equations | 解一次方程

📚 Solving Linear Equations | 解一次方程

Linear equations are a core part of the Cambridge KS3 Mathematics curriculum. In this article, you will learn how to solve one-step, two-step and multi-step equations, how to check your answers, and how to avoid common mistakes.

一次方程是剑桥 KS3 数学课程的核心内容。在本文中，你将学习如何解一步、两步和多步方程，如何检验答案，以及如何避免常见错误。

1. Understanding Equations | 理解方程

An equation is a mathematical statement that two expressions are equal. It always contains an equals sign. For example, 2x + 3 = 11 is an equation, while 2x + 3 is just an expression.

方程是表示两个表达式相等的数学语句。它总是包含等号。例如，2x + 3 = 11 是一个方程，而 2x + 3 只是一个表达式。

In KS3, most equations are linear. A linear equation has the unknown raised to the power of 1 only. Examples include 5x – 2 = 13 and 7 = 2x + 1. Equations such as x² + 2 = 6 are not linear because the variable is squared.

在 KS3 阶段，大多数方程是一次方程。一次方程中未知数的次数仅为 1。例如 5x – 2 = 13 和 7 = 2x + 1。像 x² + 2 = 6 这样的方程不是一次方程，因为变量出现了平方。

2. Using Inverse Operations | 使用逆运算

To solve an equation, we need to isolate the unknown. This is done by applying inverse operations. Addition and subtraction are inverses, and multiplication and division are inverses.

解方程时，我们需要将未知数单独留在等号一边。这可以通过逆运算来实现。加法和减法互为逆运算，乘法和除法互为逆运算。

The balance method is the key idea. Whatever operation you perform on one side of the equation, you must perform the same operation on the other side. This keeps the equation balanced.

平衡法是关键思想。无论你对等式的一边进行什么运算，都必须对另一边进行相同的运算。这样才能保持方程平衡。

3. Solving One-Step Equations | 解一步方程

Example: Solve x + 7 = 15. To undo the addition of 7, subtract 7 from both sides:

例题：解方程 x + 7 = 15。为了消去加 7，两边同时减去 7：

x + 7 – 7 = 15 – 7 ⇒ x = 8

Example: Solve 4x = 20. To undo multiplication by 4, divide both sides by 4:

例题：解方程 4x = 20。为了消去乘以 4，两边同时除以 4：

4x ÷ 4 = 20 ÷ 4 ⇒ x = 5

Example: Solve x ÷ 3 = 6. To undo division by 3, multiply both sides by 3:

例题：解方程 x ÷ 3 = 6。为了消去除以 3，两边同时乘以 3：

x ÷ 3 × 3 = 6 × 3 ⇒ x = 18

4. Solving Two-Step Equations | 解两步方程

A two-step equation requires two inverse operations. For example, solve 2x + 3 = 11. First subtract 3 from both sides because addition is the outer operation.

两步方程需要两次逆运算。例如，解方程 2x + 3 = 11。首先两边同时

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