📚 Solving Linear Equations | 解一元一次方程
Linear equations are the foundation of algebra. A linear equation is a statement that two expressions are equal, and it usually involves an unknown variable, commonly represented by a letter such as x. In KS3 mathematics, you learn to solve these equations by applying inverse operations and maintaining balance, much like keeping a set of scales level. Mastering this skill is essential for handling more complex problems in algebra, geometry, and real‑life situations.
一元一次方程是代数的基础。方程是两个表达式相等的陈述，通常含有一个用字母（如 x）表示的未知数。在 KS3 数学中，你将学习通过逆运算和保持等式平衡（就像天平一样）来解方程。掌握这一技能对于应对代数、几何以及现实生活中的更复杂问题至关重要。
1. What Is a Linear Equation? | 什么是一元一次方程？
he power of 1. It can be written in forms like x + 3 = 7, 4x = 20, or 2x − 5 = 9. The word 'linear' on solving these equations to find the value of the unknown that makes the equation true.
一元一次方程是指未知数的指数仅为 1 的方程。它可以写成 x + 3 = 7、4x = 20 或 2x − 5 = 9 等形式。“线性”一词源于其图像是一条直线。在 KS3 阶段，我们重点学习解这类方程，找出使等式成立的未知数的值。
2. Balancing Method | 平衡法
Think of an equation as a pair of scales in perfect balance. Whatever you do to one side, you must do exactly the same to the other side to keep the scales balanced. This is the golden rule of algebra: if you add, subtract, multiply, or divide on one side, you must perform the same operation on the other side. The balancing method helps you isolate the unknown step by step.
把方程想象成一对完全平衡的天平。无论你对一边做了什么，都必须对另一边做完全相同的操作，以保持平衡。这是代数的黄金法则：如果你在一边进行加、减、乘、除，你必须在另一边执行相同的运算。平衡法有助于你一步步地分离出未知数。
3. Solving with Addition and Subtraction | 用加法和减法解方程
11. Always write the solution clearly and check by substituting it back into the original equation.
当一个数被加到或减去未知数时，可用逆运算消去该数。例如，在 x + 5 = 12 中，两边同时减去 5，得到 x = 7。同样地，对于 x − 3 = 8，两边同时加 3，得出 x = 11。始终清晰写出解，并通过代入原方程进行检查。
4. Solving with Multiplication and Division | 用乘法和除法解方程
member that multiplication and division are inverse operations, just like addition and subtraction.
如果未知数乘以一个数，则两边同时除以该数。例如，3x = 18 除以 3 后得 x = 6。如果未知数除以一个数，则两边同时乘以该数。对于 x/4 = 5，乘以 4 得 x = 20。记住乘法和除法互为逆运算，就像加法和减法一样。
5. Two‑Step Equations | 两步方程
Two‑ vide both sides by 2 to find x = 4. Always work backwards through the order of operations.
两步方程涉及运算组合，例如 2x + 3 = 11。解这类方程时，先消去加减法，再消去乘除法。对于 2x + 3 = 11，两边减 3 得 2x = 8，然后两边除以 2，得 x = 4。始终逆着运算顺序来求解。
6. Equations with Brackets | 带括号的方程
divide both sides by the factor outside. Expanding gives 3x + 6 = 15, then solve as a two‑ + 2 = 5, which quickly yields x = 3. Choose the method that makes the arithmetic simpler.
当方程含有括号时，如 3(x + 2) = 15，你可以先展开括号，也可以两边先除以括号外的系数。展开得 3x + 6 = 15，然后按两步方程求解。或者，两边除以 3 得 x + 2 = 5，立即求出 x = 3。选择使计算更简单的方法。
7. Equations with Unknowns on Both Sides | 未知数在方程两边的情况
d finally x = 3. Always aim to simplify by eliminating the smaller coefficient of x first.
在 5x − 2 = 3x + 4 这类方程中，未知数出现在两边。目标是把所有含 x 的项移到一边，把所有常数项移到另一边。两边同时减 3x，得 2x − 2 = 4，然后两边加 2 得 2x = 6，最后 x = 3。通常先消去 x 系数较小的一边来简化。
8. Forming Equations from Word Problems | 从应用题列方程
Many real‑ n quantity, and express the given relationships using algebraic expressions. For instance, 'Three times a number plus four equals nineteen' o 3n + 4 = 19. Then solve and interpret the answer in context, making sure it makes sense.
许多现实情境都可以用线性方程来建模。仔细阅读题目，确定未知量，并用代数表达式表示已知关系。例如，“某个数的三倍加四等于十九”可列出 3n + 4 = 19。然后求解并在上下文中解释答案，确保其合理。
9. Checking Your Solution | 检验你的解
= 8 + 5 = 13, which matches. This habit prevents careless mistakes and builds confidence.
求出解后，始终将其代回原方程进行验证。如果两边相等，则解是正确的。例如，解出 2x + 5 = 13 得到 x = 4，检验：2(4) + 5 = 8 + 5 = 13，相符。这个习惯可以避免粗心错误，并建立信心。
10. Common Mistakes to Avoid | 要避免的常见错误
expanding brackets, ensure you multiply every term inside. Also, when moving terms, remember to change signs correctly. Practise carefully to build accuracy.
学习者常常忘记对两边进行同等操作。另一个常见错误是处理负号不当，例如把 −x = 5 错误地解为 x = 5 而不是 x = −5。展开括号时，确保乘以括号内的每一项。移项时，要正确变号。仔细练习以提高准确性。
11. Practice Examples with Step‑by‑Step | 带步骤的练习例子
Let's work through some typical KS3 questions. Example 1: Solve 4x − 7 = 13. Add 7 to both sides → 4x = 20, divide by 4 → x = 5. Example 2: , subtract 6 → −12 = 2x, divide by 2 → x = −6. Always follow the balancing rule and check.
让我们完成一些典型的 KS3 题目。例 1：解 4x − 7 = 13。两边加 7 → 4x = 20，除以 4 → x = 5。例 2：解 3(x − 2) = 5x + 6。展开 → 3x − 6 = 5x + 6，减 3x → −6 = 2x + 6，减 6 → −12 = 2x，除以 2 → x = −6。始终遵循平衡法则并检验。
12. Summary | 小结
Solving linear equations is a core algebra skill that relies on the balancing method and inverse operations. By mastering one‑step, two‑step, bracket, and variable‑on‑both‑sides equations, you build a strong foundation for higher‑level mathematics. Consistent practice and checking your solutions will make equation solving automatic and enjoyable.
解一元一次方程是一项核心代数技能，它依赖于平衡法和逆运算。通过掌握一步方程、两步方程、带括号的方程以及两边都有未知数的方程，你为更高级的数学打下了坚实基础。持续练习并检验你的解将使解方程变得熟练且有趣。
Published by TutorHao | Mathematics Revision Series | aleveler.com
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