📚 Cambridge KS3 Mathematics: Solving Linear Equations | 剑桥KS3数学：一元一次方程求解
Linear equations are a central part of the Cambridge KS3 mathematics course. They help students understand the idea of an unknown value and how to find it using logical steps. This article will guide you through the balance method, inverse operations, brackets, fractions and word problems.
一元一次方程是剑桥 KS3 数学课程的核心内容。它帮助学生理解未知数的概念，以及如何通过有逻辑的步骤求出未知数。本文将带你掌握天平平衡法、逆运算、括号、分数和文字题。
1. What Is an Equation? | 什么是方程
ple, in x + 5 = 12, the letter x stands for the number that must be added to 5 to make 12.
方程是说明两个表达式相等的数学语句。它包含等号，并且常常含有一个字母，如 x 或 y，用来表示未知数。例如，在 x + 5 = 12 中，字母 x 代表与 5 相加后等于 12 的那个数。
x + 5 = 12 ⇒ x = 7
Here x = 7 because 7 + 5 = 12. This is called the solution of the equation.
这里 x = 7，因为 7 + 5 = 12。这个值就叫做方程的解。
2. The Balance Method | 天平平衡法
Think of an equation as a balanced scale. The left side and the right side must always have the same value. If you add, subtract, multiply or divide, you must do exactly the same to both sides. This keeps the equation balanced while you isolate the unknown.
把方程想象成一架平衡的天平。左边和右边的值必须始终相等。如果你进行加、减、乘或除的运算，必须在等号两边进行完全相同的操作。这样可以在保持方程平衡的同时，把未知数单独解出来。
0, you cannot simply remove the 3 from the left side. You must subtract 3 from both sides:
例如，如果 x + 3 = 10，不能只把左边的 3 去掉，而必须两边同时减去 3：
x + 3 − 3 = 10 − 3 ⇒ x = 7
This 'same operation on both sides' idea is the most important rule in solving equations.
这种 "两边同时进行相同运算" 的思路是解方程最重要的规则。
3. Using Inverse Operations | 运用逆运算
Inverse operations are opposite operations that undo each other. Addition and subtraction are inverse operations, and multiplication and division are inverse operations. To solve an equation, we use inverse operations to 'undo' what has been done to the unknown.
逆运算是互相对立、可以相互抵消的运算。加法和减法互为逆运算，乘法和除法互为逆运算。解方程时，我们使用逆运算来 "抵消" 对未知数所做的操作。
- If x has 5 added to it, subtract 5 from both sides.
- 如果 x 被加上了 5，就两边同时减去 5。
- If x is multiplied by 4, divide both sides by 4.
- 如果 x 被乘了 4，就两边同时除以 4。
This method turns a complicated equation into a simple statement such as x = 8.
这种方法可以把一个复杂的方程变成一个简单的结果，例如 x = 8。
4. Solving by Adding or Subtracting | 通过加减求解
When a number is added to or subtracted from the unknown, use the opposite operation to remove it. Always perform the operation on both sides.
当一个数加在未知数上或从未知数中减去时，使用相反的运算把它消掉。务必在等号两边同时进行该运算。
Example 1: Solve x − 7 = 15.
例 1：解 x − 7 = 15。
x − 7 + 7 = 15 + 7 ⇒ x = 22 Published by TutorHao | KS3 Mathematics Revision Series | aleveler.com
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