📚 Solving Linear Equations: Balance, Brackets and Beyond | 解一元一次方程：等式平衡、去括号与进阶技巧
Linear equations are the foundation of algebra at KS3. They appear in number puzzles, geometry problems and real-life calculations. This article walks you through the balancing method, one-step and two-step equations, brackets, unknowns on both sides, fractions and word problems, with fully worked examples and common mistakes to avoid.
一元一次方程是 KS3 代数的基础。它们出现在数字谜题、几何问题和现实计算中。本文将带你系统学习等式平衡法、一步与两步方程、去括号、两边含未知数、含分数方程和应用题，并配有完整例题和常见错误提醒。
1. What Is a Linear Equation? | 什么是一元一次方程？
roots or products of unknowns. For example, 2x + 3 = 11 is linear, but x² + 3 = 11 is not.
一元一次方程是指未知数（通常写作 x）的指数仅为 1 的方程。方程中不会出现 x²、x³、平方根或未知数相乘的情形。例如 2x + 3 = 11 是一元一次方程，而 x² + 3 = 11 不是。
The word 'linear' 2x + 3, you get a straight line. At KS3, solving a linear equation means finding the value of x that makes the equation true.
'线性' 一词来源于：若画出 y = 2x + 3 的图像，你会得到一条直线。在 KS3 阶段，解一元一次方程就是求出使等式成立的 x 的值。
- Equation: 2x + 3 = 11 — 方程：2x + 3 = 11
- Expression: 2x + 3 — 表达式：2x + 3
- Solution: x = 4 because 2(4) + 3 = 11 — 解：x = 4，因为 2(4) + 3 = 11
2. The Balancing Method | 等式平衡法
Think of an equation as a balance scale. The left side and right side have equal weight. Whatever you do to one side, you must do to the other side to keep the equation balanced.
把方程想象成一个天平。左边和右边的重量相等。无论你对一边做什么运算，都必须对另一边做同样的运算，才能保持等式平衡。
If you add, subtract, multiply or divide by the same non-zero number on both sides, the equation remains true. This is the golden rule behind all the methods in this article.
如果你在方程两边同时加、减、乘或除以同一个非零数，方程仍然成立。这是本文所有方法背后的黄金法则。
Golden rule: Do the same to both sides. —— 黄金法则：等式两边同时进行相同运算。
- Example: If x = 5, then x + 2 = 5 + 2, so x + 2 = 7. — 例如：若 x = 5，则 x + 2 = 5 + 2，所以 x + 2 = 7。
- Example: If 3x = 12, then 3x ÷ 3 = 12 ÷ 3, so x = 4. — 例如：若 3x = 12，则 3x ÷ 3 = 12 ÷ 3，所以 x = 4。
3. Solving One-Step Equations | 解一步方程
A one-step equation only needs one inverse operation to isolate x. The inverse of addition is subtraction, and the inverse of multiplication is division.
一步方程只需一步逆运算就能求出 x。加法的逆运算是减法，乘法的逆运算是除法。
For x + 5 = 12, subtract 5 from both sides: x + 5 − 5 = 12 − 5, so x = 7.
对于 x + 5 = 12，两边同时减 5：x + 5 − 5 = 12 − 5，所以 x =
Published by TutorHao | KS3 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