📚 Solving Linear Equations (Page 201, Question 2) | 解一元一次方程（第201页第2题）
Welcome to this Cambridge KS3 revision lesson. The question on page 201, question 2, asks you to solve a linear equation. This article explains every skill you need and shows how to avoid common errors.
欢迎来到这节 Cambridge KS3 数学复习课。第201页第2题要求你解一个一元一次方程。本文将讲解你需要掌握的每一项技能，并告诉你如何避免常见错误。
1. Reading the Question on Page 201 | 读懂第201页第2题
Before writing anything, read the full question. Identify the unknown, usually labelled x, the operations applied to it, and the value of the expression.
动笔之前，先通读全题。找出未知数（通常用 x 表示）、对它施加了哪些运算，以及整个表达式的值。
The equation is a statement that two expressions are equal. Your job is to find the value of the unknown that makes the statement true.
方程是说明两个表达式相等的一个陈述。你的任务是求出使这个陈述成立的未知数的值。
Underline the equals sign and circle the variable. This helps you focus on keeping the equation balanced.
在等号下面画线，把变量圈出来。这样可以帮助你专注于保持方程左右平衡。
2. What Is a Linear Equation? | 什么是一元一次方程
variable has the general form ax + b = c, where a, b and c are numbers and a is not zero.
一元一次方程的一般形式是 ax + b = c，其中 a、b、c 是数字，且 a 不等于 0。
The word linear means the variable has power one. There are no x², x³ or 1/x terms in a linear equation.
"一次" 表示变量的次数为 1。一元一次方程中不会出现 x²、x³ 或 1/x 这样的项。
For example, 3x − 4 = 11 is linear, but x² + 2 = 6 is not linear.
例如，3x − 4 = 11 是一元一次方程，但 x² + 2 = 6 不是一次方程。
Recognising this structure helps you choose the right method before you start solving.
先识别方程的结构，有助于你在开始求解前选对方法。
3. The Balance Method | 天平法
Think of an equation as a balanced set of scales. The left-hand side and the right-hand side must remain equal.
把方程想象成一架平衡的天平。左边和右边必须始终保持相等。
Whatever you do to one side, you must do to the other side. This is the golden rule of equation solving.
你对一边做什么运算，就必须对另一边做同样的运算。这是解方程的黄金法则。
x + 5 = 12
For x + 5 = 12, subtract 5 from both sides: x + 5 − 5 = 12 − 5, so x = 7.
对于 x + 5 = 12，两边同时减去 5：x + 5 − 5 = 12 − 5，因此 x = 7。
Using the balance method reduces mistakes because every step has a clear reason.
使用天平法能减少错误，因为每一步都有明确的理由。
4. Solving One-Step Equations | 解一步方程
A one-step equation needs only one inverse operation. Addition and subtraction are inverse operations.
一步方程只需要一次逆运算。加法和减法互为逆运算。
For x − 3 = 8, add 3 to both sides: x = 11.
对于 x − 3 = 8，两边同时加 3：x = 11。
nd division are also inverse operations. For 4x = 20, divide both sides by 4 to get x = 5.
乘法和除法也互为逆运算。对于 4x = 20，两边同时除以 4，得到 x = 5。
For x/5 = 3, multiply both sides by 5 to get x = 15.
对于 x/5 = 3，两边同时乘以 5，得到 x = 15。
Always write the final answer as x = value, not value = x, to match the expected form.
最终答案始终写成 x = 数值，而不是 数值 = x，以符合标准书写形式。
5. Solving Two-Step Equations | 解两步方程
A two-step equation has two operations on the variable, such as 3x + 4 = 19.
两步方程对变量进行了两次运算，例如 3x + 4 = 19。
Undo the addition or subtraction first, then undo the multiplication or division.
先逆着做加法或减法，再逆着做乘法或除法。
Step 1: subtract 4 from both sides. 3x + 4 − 4 = 19 − 4, so 3x = 15.
步骤1：两边同时减去 4。3x + 4 − 4 = 19 − 4，得到 3x = 15。
Step 2: divide both sides by 3. 3x ÷ 3 = 15 ÷ 3, so x = 5.
步骤2：两边同时除以 3。3x ÷ 3 = 15 ÷ 3，因此 x = 5。
This reverse order follows the opposite of BODMAS: undo adding or subtracting before multiplying or dividing.
这个逆序正好与 BODMAS 相反：先逆加减，再逆乘除。
ched to the number. For 2x − 5 = −9, add 5 to get 2x = −4, then divide by 2 to get x = −2.
遇到负数时，符号要跟着数字走。对于 2x − 5 = −9，两边加 5 得到 2x = −4，再除以 2 得到 x = −2。
6. Equations with Brackets | 带括号的方程
If an equation contains brackets, expand them first or divide by the factor outside the bracket.
如果方程中有括号，可以先去括号，也可以先除以括号外的系数。
2(x + 3) = 14
For 2(x + 3) = 14, expanding gives 2x + 6 = 14.
对于 2(x + 3) = 14，去括号得到 2x + 6 = 14。
Then subtract 6 from both sides: 2x = 8. Finally divide by 2: x = 4.
然后两边同时减去 6：2x = 8。最后两边同时除以 2：x = 4。
Another method is to divide both sides by 2 first: x + 3 = 7, so x = 4.
另一种方法是先两边同时除以 2：x + 3 = 7，所以 x = 4。
Both methods give the same answer. Choose the one that looks easier for the specific equation.
两种方法得到相同答案。选择对具体方程更简单的一种即可。
7. Equations with the Variable on Both Sides | 未知数在等式两边
Some equations have the variable on both sides, such as 5x − 2 = 2x + 7.
有些方程的未知数出现在等号两边，例如 5x − 2 = 2x + 7。
Your strategy is to collect all variable terms on one side and all number terms on the other side.
解题策略是把所有含未知数的项移到一边，所有数字项移到另一边。
Subtract 2x from both sides: 5x − 2 − 2x = 2x + 7 − 2x, which gives 3x − 2 = 7.
两边同时减去 2x：5x − 2 − 2x = 2x + 7 − 2x，得到 3x − 2 = 7。
Then add 2 to both sides: 3x = 9. Divide by 3 to find x = 3.
然后两边同时加 2：3x = 9。再除以 3，得到 x = 3。
Avoid moving terms without changing signs. Use inverse operations and write every step clearly.
避免不移项却不改符号。使用逆运算，并把每一步写清楚。
8. Working
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