📚 Solving Equations Step by Step: Practice 120 Question 1 | 解方程分步详解：练习120第1题
Equations are at the heart of KS3 Mathematics. Being able to solve linear equations confidently will help you tackle everything from number problems to geometry and real‑life puzzles. In this article we take a typical Cambridge KS3 practice question – ‘Solve 3(x – 2) + 4 = 19’ – and break it into clear, manageable steps. You will not only see exactly how to find the value of x, but also learn why each step works and how to avoid the most common slip‑ups.
方程是 KS3 数学的核心。能够自信地解一次方程，不仅能帮你解决数字问题，还能应对几何和现实生活中的各种谜题。本文我们将以一道典型的剑桥 KS3 练习题——‘解方程 3(x – 2) + 4 = 19’——为例，把它拆解成清晰、易操作的步骤。你不仅会看到 x 的具体求法，还能理解每一步为什么正确，并学会避开最常见的错误。
1. What is a Linear Equation? | 什么是一次方程？
A linear equation is an equation where the unknown (usually x) is only raised to the power of 1. It can contain brackets, fractions and constants, but no x² or higher powers. Linear equations can always be rearranged into the form ax + b = c, where a, b and c are numbers.
一次方程是未知数（通常是 x）只出现一次幂的方程。它可以包含括号、分数和常数，但不会出现 x² 或更高次幂。一次方程总可以整理成 ax + b = c 的形式，其中 a、b、c 都是数字。
2. The Sample Question from Practice 120 | 练习120的样题
The question we will solve is typical of the multi‑step equations you meet in Year 8 and Year 9: Solve 3(x – 2) + 4 = 19. It combines brackets, multiplication and addition, so it is perfect for practising balanced moves.
我们要解的题目是 8 年级和 9 年级常见的多步方程：解方程 3(x – 2) + 4 = 19。题目里既有括号，又有乘法和加法，非常适合用来练习等式的平衡变形。
3. Step 1 – Expand Brackets Correctly | 第1步 – 正确展开括号
Always begin by removing any brackets. Multiply the term outside the bracket by every term inside. Here, 3 must multiply both ‘x’ and ‘–2’: 3 × (x – 2) = 3x – 6. The equation then becomes 3x – 6 + 4 = 19. Miss this step and you risk losing marks for an otherwise simple question.
解题总是从去掉括号开始。用括号外的项去乘括号里的每一项。这里，3 必须同时乘 x 和 –2：3 × (x – 2) = 3x – 6。于是方程变为 3x – 6 + 4 = 19。跳过这一步，很可能在本来简单的题目上丢分。
4. Step 2 – Simplify Like Terms | 第2步 – 合并同类项
After expanding, look for numbers that can be combined. We have –6 and +4 on the left side; together they make –2. The equation now reads 3x – 2 = 19. Simplifying early reduces the number of steps and keeps your working neat.
展开括号后，找出可以合并的数字项。左边有 –6 和 +4，它们结合后变成 –2。方程现在就变为 3x – 2 = 19。尽早化简可以减少步骤，保持卷面整洁。
5. Step 3 – Isolate the x‑term by Balancing | 第3步 – 通过等式平衡分离含 x 项
We want the term with x (3x) alone on one side. To remove the ‘–2’ we do the inverse operation: add 2 to both sides of the equation. 3x – 2 + 2 = 19 + 2 gives 3x = 21. Keeping the equation balanced is the golden rule – whatever you do to one side you must do to the other.
我们希望含 x 的项（3x）单独在等号一边。要去掉 ‘–2’，就要做逆运算：在方程两边同时加 2。3x – 2 + 2 = 19 + 2 得到 3x = 21。保持等式平衡是黄金法则——对等号一边做了什么，另一边也必须做同样的运算。
6. Step 4 – Divide to Find x | 第4步 – 用除法求出 x
The unknown x is now being multiplied by 3. The inverse of multiplication is division, so divide both sides by 3: 3x ÷ 3 = 21 ÷ 3 → x = 7. This gives the solution: x equals seven.
此时未知数 x 被乘了 3，乘法的逆运算是除法，因此两边同时除以 3：3x ÷ 3 = 21 ÷ 3 → x = 7。这样我们就得到了解：x 等于 7。
7. Step 5 – Check Your Answer in the Original Equation | 第5步 – 将答案代回原方程检验
Never skip the check. Replace x with 7 in the original equation 3(x – 2) + 4: inside the bracket, 7 – 2 = 5; times 3 gives 15; plus 4 gives 19. The right‑hand side is indeed 19, so the solution is correct. Checking catches careless errors and builds confidence.
千万不要跳过检验。把 x = 7 代入原方程 3(x – 2) + 4：括号内 7 – 2 = 5；乘以 3 得 15；再加 4 得 19。等号右边正是 19，因此答案正确。检验能揪出粗心错误，也能让自己更有信心。
8. Common Mistakes and How to Avoid Them | 常见错误及避免方法
Two frequent errors are: forgetting to multiply every term inside the bracket (some only multiply the first term), and forgetting to keep the operation balanced – e.g. adding only on the left. Using a step‑by‑step grid or a checklist can dramatically reduce these slip‑ups.
两个最常见的错误是：忘记乘括号里的每一项（不少人只乘了第一项），以及忘记保持等式平衡——比如只在左边加了一个数。按步骤列网格或使用检查清单，可以大幅减少这类失误。
| Mistake | Correction |
|---|---|
| 3(x – 2) → 3x – 2 (missed multiplying –2 by 3) | Always rewrite as 3x – 6 |
| Adding 2 only to one side | Apply the same operation to both sides |
中文对照：
| 错误 | 纠正方法 |
|---|---|
| 3(x – 2) → 3x – 2（忘了将 –2 也乘 3） | 始终写成 3x – 6 |
| 只在一侧加 2 | 必须在等号两边同时加 2 |
9. Practising with Similar Questions | 用类似题目进行练习
To master the method, try variations such as 4(2x – 1) + 3 = 23 or 5(x + 6) – 8 = 37. Start by expanding, then simplify, balance and divide. Keep a record of your steps and always check your answer at the end.
要真正掌握这种方法，可以试着挑战变式题，比如 4(2x – 1) + 3 = 23 或 5(x + 6) – 8 = 37。同样从展开括号开始，再化简、平衡、除以系数。记录每一步的变形，并在最后检验答案。
10. How Equations Connect to Real Life | 方程与现实生活的联系
Equations aren’t just abstract puzzles. When you calculate how many weeks you need to save £50 if you already have £35 and save £3 a week, you are solving the equation 3w + 35 = 50. The same balanced‑step logic applies whether you are planning a budget, mixing ingredients or sharing costs.
方程并不是抽象的谜题。如果你已有 35 英镑，每周存 3 英镑，计算需要多少周才能存到 50 英镑时，你就在解方程 3w + 35 = 50。无论是规划预算、调配食材还是分摊费用，都可以用到相同的等式平衡逻辑。
11. Your Step‑by‑Step Toolkit | 你的分步解题工具箱
You can now approach any similar linear equation with this five‑step routine: expand → simplify → balance → divide → check. Writing these steps as a checklist on a revision card can turn a multi‑step problem into a simple, automatic process.
现在，你可以用这五个常规步骤来对付任何类似的一次方程：展开 → 化简 → 平衡 → 除以系数 → 检验。把这些步骤写成复习卡片上的检查清单，就能把多步问题变成一个简单、自动化的流程。
12. Key Points to Remember for Your Test | 考试中要牢记的重点
- Brackets first: always multiply every term inside by the number outside.
- Balance: whatever operation you do, do it to both sides.
- Inverse operations: add when you see subtraction, divide when you see multiplication.
- Check: substitute your answer back into the original equation and verify.
If you can lock in these habits, you will handle even the trickiest KS3 equations with ease.
- 先处理括号：一定要用外面的数去乘括号里的每一项。
- 保持平衡：无论进行什么运算，等号两边都要同步操作。
- 使用逆运算：见到减法就加，见到乘法就除。
- 验证：把答案代回原方程，确认成立。
养成这些习惯，再难的 KS3 方程也能轻松应对。
Published by TutorHao | Mathematics Revision Series | aleveler.com
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