Cambridge KS3 Maths Page 144 Question 2: Solving Linear Equations with Brackets | 剑桥 KS3 数学第144页第2题：解带括号的一元一次方程

📚 Cambridge KS3 Maths Page 144 Question 2: Solving Linear Equations with Brackets | 剑桥 KS3 数学第144页第2题：解带括号的一元一次方程

Welcome to this Cambridge KS3 Mathematics revision article based on page 144, question 2. The question asks you to solve a linear equation with brackets, and many students lose marks not because they cannot solve it, but because they rush the first step. Here we will break the method into small, reliable stages.

欢迎阅读这篇基于第144页第2题的剑桥 KS3 数学复习文章。题目要求你解一个含有括号的一元一次方程，许多学生丢分并不是因为不会解，而是因为第一步太着急。下面我们将把解题方法拆分成小而可靠的步骤。

1. Understanding the Task | 理解题目要求

Start by identifying the exact type of equation. A linear equation has the variable x raised only to the power 1. Brackets such as 3(x − 2) must be expanded before you can see all the terms clearly.

首先判断方程的类型。一元一次方程中变量 x 的指数仅为 1。像 3(x − 2) 这样的括号必须先展开，才能清楚地看到所有项。

In this example, the unknown appears on both sides of the equals sign. That means you will need to collect x terms on one side and constant terms on the other.

在这个例子中，未知数出现在等号两边。这意味着你需要把含 x 的项集中到一边，把常数项集中到另一边。

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2. Key Vocabulary | 关键术语

Before solving, make sure you understand these key words. They appear frequently in Cambridge KS3 tests and Checkpoint papers.

在解题之前，请确保理解下面这些关键词。它们经常出现在剑桥 KS3 测试和 Checkpoint 试卷中。

Term	Meaning
Equation	A statement that two expressions are equal
Unknown	The letter, usually x, whose value you need to find
Expand	Multiply out a bracket using the outside number
Collect like terms	Gather x terms or number terms together
Balance method	Do the same operation to both sides

Memorising these terms helps you follow written instructions and explain your method accurately.

记住这些术语有助于你理解题目指令并准确解释解题方法。

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3. Expanding Brackets First | 先展开括号

ou must multiply both terms inside the bracket by 3: first 3 × x = 3x, then 3 × (−2) = −6.

表达式 3(x − 2) 表示 3 乘以整个括号。你必须把括号内的两项都乘以 3：先算 3 × x = 3x，再算 3 × (−2) = −6。

3(x − 2) = 3x − 6

Never write 3x − 2 after expanding. That mistake means you only multiplied the x term and forgot the −2, which changes the equation completely.

展开后绝不能写成 3x − 2。这个错误表示你只乘了 x 项，忘记了 −2，这会完全改变方程。

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4. Rewriting the Equation After Expansion | 展开后重新写下方程

so both sides are clear. The original equation 3(x − 2) = 2x + 5 becomes 3x − 6 = 2x + 5.

括号展开后，重新写下完整的方程，使两边都清晰可见。原方程 3(x − 2) = 2x + 5 变为 3x − 6 = 2x + 5。

3x − 6 = 2x + 5

At this stage, do not try to do several operations at once. Keeping the equation neat reduces sign errors.

在这个阶段，不要试图同时进行多步运算。保持方程整洁可以减少符号错误。

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5. Collecting x Terms on One Side | 把含 x 的项集中到一边

m both sides. The left becomes 3x − 2x − 6 = x − 6, and the right becomes 2x − 2x + 5 = 5.

你需要把含 x 的项集中到一边。两边同时减去 2x。左边变为 3x − 2x − 6 = x − 6，右边变为 2x − 2x + 5 = 5。

3x − 6 − 2x = 2x + 5 − 2x ⇒ x − 6 = 5

Remember the balance method: whatever you do to one side, you must do to the other. This keeps the equation true.

记住天平法：对一边做什么运算，另一边也必须做同样的运算。这样才能保持等式成立。

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6. Isolating the Variable | 分离变量

sides to isolate x. On the left, −6 + 6 = 0, so only x remains. On the right, 5 + 6 = 11.

现在两边同时加上 6，把 x 单独留在左边。左边 −6 + 6 = 0，所以只剩下 x。右边 5 + 6 = 11。

x − 6 + 6 = 5 + 6 ⇒ x = 11

nal answer clearly as x = 11. In a test, write this on the answer line if one is provided.

最后答案要清楚地写成 x = 11。在考试中，如果题目有答案横线，请把答案写在横线上。

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7. Checking Your Solution | 检验答案

h 11. The left side is 3(11 − 2) = 3 × 9 = 27. The right side is 2 × 11 + 5 = 22 + 5 = 27.

代入是检验答案最快的方法。把原方程中的每个 x 替换为 11。左边为 3(11 − 2) = 3 × 9 = 27。右边为 2 × 11 + 5 = 22 + 5 = 27。

LHS = 27 and RHS = 27

Because both sides are equal, the solution is verified. Always do this when you have spare time in an assessment.

因为两边相等，所以答案得到验证。在测评中只要有空余时间，就一定要检验。

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8. Common Mistakes to Avoid | 常见错误

Watch out for these common errors. They often appear in marked work and can cost easy marks.

请注意以下常见错误。它们经常出现在批改过的

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