📚 Solving Linear Equations | 解一元一次方程
In KS3 Cambridge Mathematics, linear equations appear in many forms: one-step, two-step, with brackets, with fractions, and with variables on both sides. Building a clear and systematic method now will make later topics such as sequences, graphs and problem solving much easier.
在剑桥 KS3 数学中，一元一次方程以多种形式出现：一步方程、两步方程、带括号、含分数以及两边都有未知数的方程。现在建立清晰、系统的方法，会让后续的数列、图像和问题解决等主题更容易。
1. What Is a Linear Equation? | 什么是一元一次方程？
A linear equation is an algebraic statement in which two expressions are equal, and the unknown variable appears only to the first power. This means you will never see x², x³, or variables multiplied together in a KS3 linear equation.
一元一次方程是一种代数等式，其中两个表达式相等，并且未知数只以一次幂出现。这意味着在 KS3 的一元一次方程中，你不会看到 x²、x³ 或变量相乘。
Typical examples include 2x + 3 = 7, x/4 − 1 = 2 and 3(x − 2) = 15. They look different, but all can be solved by using inverse operations.
典型例子包括 2x + 3 = 7、x/4 − 1 = 2 和 3(x − 2) = 15。它们看起来不同，但都可以通过逆运算来求解。
2. Equations as Balances | 方程如同天平
Think of an equation as a balance scale. The left-hand side (LHS) and the right-hand side (RHS) must stay equal. Whatever operation you perform on one side, you must also perform on the other.
把方程想象成一个天平。左边（LHS）和右边（RHS）必须始终保持相等。你对其中一边进行任何运算，都必须对另一边也进行相同的运算。
2x + 3 = 9
Subtract 3 from both sides: 2x = 6. Then divide both sides by 2: x = 3. The balance remains true at every step.
两边同时减去 3：2x = 6。然后两边同时除以 2：x = 3。每一步天平都保持平衡。
Key point: whatever you do to one side of an equation, you must do exactly the same to the other side.
要点：对等式的一边做什么，对另一边也必须做完全相同的运算。
3. One-Step Equations: Addition and Subtraction | 一步方程：加法和减法
To solve x + 7 = 12, identify the operation attached to x. Since 7 is added, use the inverse operation and subtract 7 from both sides.
要解 x + 7 = 12，先找出与 x 相连的运算。因为加上了 7，所以使用逆运算，在两边同时减去 7。
x + 7 = 12 → x = 5
Similarly, for y − 4 = 11, add 4 to both sides to obtain y = 15. Always write the new equation after each step to show clear working.
类似地，对于 y − 4 = 11，两边同时加上 4，得到 y = 15。每一步之后都要写出新的方程，以展示清晰的解题过程。
The inverse of addition is subtraction; the inverse of subtraction is addition.
加法的逆运算是减法；减法的逆运算是加法。
4. One-Step Equations: Multiplication and Division | 一步方程：乘法和除法
When a variable is multiplied or divided, use the opposite operation. For 4n = 28, divide both sides by 4 because n is multiplied by 4.
当变量被乘或被除时，使用相反的运算。对于 4n = 28，因为 n 乘以 4，所以两边同时除以 4。
4n = 28 → n = 7
For m/3 = 8, the variable is divided by 3, so multiply both sides by 3. This gives m = 24.
对于 m/3 = 8，变量被 3 除，所以两边同时乘以 3。这样得到 m = 24。
The inverse of multiplication is division; the inverse of division is multiplication.
乘法的逆运算是除法；除法的逆运算是乘法。
5. Two-Step Equations | 两步方程Published by TutorHao | KS3 Mathematics Revision Series | aleveler.com
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