Solving Linear Equations: Cambridge KS3 Exercise 94.2 | 解线性方程：剑桥 KS3 练习 94.2

📚 Solving Linear Equations: Cambridge KS3 Exercise 94.2 | 解线性方程：剑桥 KS3 练习 94.2

Linear equations are one of the most important algebra skills in the Cambridge Lower Secondary Mathematics course. Exercise 94.2 focuses on using the balance method and inverse operations to find unknown values. This article walks through the key ideas, worked examples and common errors so you can build confidence before attempting the questions.

线性方程是剑桥初中数学课程中最重要的代数技能之一。练习 94.2 重点训练用天平法和逆运算求未知数。本文将梳理核心概念、典型例题和常见错误，帮助你在做题前建立信心。

---

1. What Is a Linear Equation? | 什么是线性方程？

x³, or fractions such as 1/x. Examples include x + 5 = 12, 3x − 4 = 11 and 2(x + 3) = 14.

线性方程是指未知数（通常用 x 表示）只出现一次方、没有 x²、x³ 或 1/x 这类形式的方程。例如 x + 5 = 12、3x − 4 = 11 和 2(x + 3) = 14。

In KS3, most linear equations involve one unknown and can be solved in a small number of steps. Being able to recognise them quickly is the first step to solving them accurately.

在 KS3 阶段，大多数线性方程只含有一个未知数，并且可以通过少量步骤解出。快速识别线性方程是准确解题的第一步。

---

2. The Balance Method | 天平法

Think of an equation as a balance. The left side and right side must remain equal. Whatever operation you perform on one side, you must also perform on the other side. This keeps the equation true while you simplify it.

把方程想象成一个天平，左边和右边必须始终保持相等。你对等号一边做任何运算，另一边也必须做同样的运算。这样才能在化简过程中保持方程成立。

• Add the same number to both sides
• Subtract the same number from both sides
• Multiply or divide both sides by the same non-zero number

例如：方程 x + 5 = 12，两边同时减 5，得到 x = 7。天平法确保每一步都不会破坏等式的平衡。

---

3. Inverse Operations | 逆运算

Solving an equation usually means undoing the operations that have been applied to x. Addition and subtraction are inverse operations, as are multiplication and division. Use the inverse operation to isolate x on one side of the equation.

解方程通常意味着逆向消除作用在 x 上的运算。加法和减法互为逆运算，乘法和除法也互为逆运算。使用逆运算可以把 x 单独留在等号一边。

Operation	Inverse Operation
+ a	− a
− a	+ a
× a	÷ a
÷ a	× a

For example, if x has been multiplied by 3, divide both sides by 3. If 4 has been added to x, subtract 4 from both sides.

例如，如果 x 被乘以 3，就将两边同时除以 3；如果 x 被加上 4，就将两边同时减去 4。

---

4. Solving One-Step Equations | 解一步方程

one inverse operation. Example: solve x + 7 = 15. Subtract 7 from both sides to get x = 8.

一步方程只需要进行一次逆运算。例如：解 x + 7 = 15。两边同时减去 7，得到 x = 8。

x + 7 = 15 → x = 8

Another example: solve 4x = 20. Divide both sides by 4 to get x = 5.

另一个例子：解 4x = 20。两边同时除以 4，得到 x = 5。

4x = 20 → x = 5

---

广告 / Sponsored

5. Solving Two-Step Equations | 解两步方程

2x + 3 = 11. First subtract 3 from both sides: 2x = 8. Then divide both sides by 2: x = 4.

两步方程需要两次逆运算。解 2x + 3 = 11。先把两边同时减去 3，得到 2x = 8；再把两边同时除以 2，得到 x = 4。

2x + 3 = 11 → 2x = 8 → x = 4

Always undo addition or subtraction before multiplication or division. This order follows the reverse of the usual order of operations.

一定要先处理加减，再处理乘除。这个顺序与通常运算顺序的逆过程一致。

---

6. Dealing with Negative Solutions | 处理负数解

ct 9 from both sides to get x = −5. Negative solutions are just as valid as positive ones.

有些方程会得到负数答案。例如：x + 9 = 4。两边同时减去 9，得到 x = −5。负数解和正数解同样有效。

= 6. Add x to both sides to get 10 = x + 6, then subtract 6 from both sides to find x = 4.

例如：解 10 − x = 6。两边同时加上 x，得到 10 = x + 6，再两边同时减去 6，得到 x = 4。

10 − x = 6 → 10 = x + 6 → x = 4

---

7. Equations with Brackets | 带括号的方程

solve 2(x + 3) = 14. Expand to 2x + 6 = 14, then subtract 6 and divide by 2 to get x = 4.

当方程含有括号时，要先去括号。例如：解 2(x + 3) = 14。先去括号得到 2x + 6 = 14，然后两边同时减去 6，再除以 2，得到 x = 4。

2(x + 3) = 14 → 2x + 6 = 14 → x = 4

Remember to multiply every term inside the bracket by the number outside. This is the distributive law at work.

记住：括号外的数要乘以括号内的每一项。这实际上就是乘法分配律的应用。

---

8. Variables on Both Sides | 两边都有未知数的方程

0. Subtract 3x from both sides: 2x + 2 = 10. Then subtract 2 and divide by 2 to get x = 4.

如果 x 出现在等号两边，要先把所有含 x 的项移到同一边。例如：解 5x + 2 = 3x + 10。两边同时减去 3x，得到 2x + 2 = 10；然后减去 2，再除以 2，得到 x = 4。

5x + 2 = 3x + 10 → 2x + 2 = 10 → x = 4

Always do the same operation to both sides when collecting like terms. This keeps the equation balanced and prevents sign errors.

合并同类项时，两边必须始终做同样的运算。这样可以保持等式平衡，避免符号错误。

---

9. Checking Your Solution | 检验你的解

your solution is correct. For x = 4 in 2x + 3 = 11: 2(4) + 3 = 8 + 3 = 11, which is true.

求出 x 后，把它代回原方程。如果左边等于右边，说明解是正确的。例如把 x = 4 代入 2x + 3 = 11：2(4) + 3 = 8 + 3 = 11，等式成立。

Checking helps catch arithmetic mistakes before you move on to the next question. It is a quick and reliable way to confirm your work.

检验可以帮助你在做下一题之前发现计算错误。这是一种快速可靠地确认答案是否正确的方法。

---

Published by TutorHao | KS3 Mathematics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）