📚 Solving Equations Step by Step: Practice 120 Question 1 | 解方程分步详解：练习120第1题
ions 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’ – d 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？
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
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‑ ed 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) – , 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‑ e → 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
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图