📚 Solving Linear Equations | 解一元一次方程
Solving linear equations is a foundational skill in algebra. It involves finding the value of an unknown, usually represented by a letter like x, that makes the equation true. This skill unlocks problem-solving across mathematics and science, from balancing chemical equations to calculating distances. In this article, we will explore step-by-step methods to solve linear equations, starting from simple one-step equations and moving to more complex types involving brackets and variables on both sides.
解一元一次方程是代数的基础技能。它要求找出使等式成立的未知数（通常用字母如 x 表示）的值。这一技能能解锁数学与科学中的问题解决，从化学方程式的配平到距离的计算。本文我们将逐步探索解方程的方法，从简单的一步方程开始，逐步深入到含括号和两边都有未知数的复杂方程。
1. What is a Linear Equation? | 什么是线性方程？
e numbers and a ≠ 0. The graph of a linear equation in two variables is a straight line, which is why it is called "linear". In Key Stage 3, we focus on equations with one variable.
线性方程是变量最高次幂为1的代数陈述。它通常可以写成 ax + b = c 的形式，其中 a、b、c 是数字且 a ≠ 0。含两个变量的线性方程的图像是一条直线，因此被称为“线性”。在Key Stage 3阶段，我们主要学习含一个变量的方程。
2. The Balance Method | 天平法
ample, if we have x + 3 = 7, we can subtract 3 from both sides to isolate x, giving x = 4.
把方程想象成一个天平。两边必须始终保持相等。无论你对一边进行什么运算，必须对另一边做完全相同的运算以保持平衡。这一原则是解方程的核心。例如，如果给出 x + 3 = 7，我们可以从两边减去3，从而分离出 x，得到 x = 4。
3. One-Step Equations Using Inverse Operations | 使用逆运算的一步方程
adding 5 to both sides. Similarly, 4x = 20 leads to x = 5 after dividing both sides by 4.
要解一步方程，使用逆运算。如果方程中有加法，就做减法。如果有乘法，就做除法。例如，x − 5 = 2 在两边加5后得 x = 7。类似地，4x = 20 在两边除以4后得 x = 5。
4. Two-Step Equations | 两步方程
3x = 9. Then divide by 3: x = 3. Always reverse the order of operations (BIDMAS backwards) – addition/subtraction before multiplication/division.
两步方程包含两种运算。策略是先消去加法或减法，再消去乘法或除法。例如，3x + 2 = 11。首先从两边减去2：3x = 9。然后除以3：x = 3。始终逆用运算顺序（BIDMAS的反向）—— 先加减后乘除。
5. Equations with Brackets | 带有括号的方程
ternatively, you could divide both sides by 2 first, but expanding is often simpler when the coefficient is an integer.
当方程含有括号时，先用分配律展开，然后照常求解。例如，2(x + 3) = 12。展开：2x + 6 = 12。减去6：2x = 6。除以2：x = 3。也可以先将两边除以2，但当系数为整数时展开通常更简单。
6. Unknown on Both Sides | 两边均含未知数
: x = 3. The goal is to collect all variable terms on one side and constants on the other.
通过向两边加或减去相同的项来消除一边的变量。例如，5x − 3 = 2x + 6。从两边减去 2x：3x − 3 = 6。加3：3x = 9。除以3：x = 3。目标是将所有含变量的项集中到一边，常数项集中到另一边。
7. Equations Involving Fractions | 涉及分数的方程
= 30 → 5x = 30 → x = 6. Always check that the solution does not make any denominator zero.
将每一项乘以最小公分母以清除分数。例如，½ x + ⅓ x = 5。2和3的最小公分母是6。全式乘以6：6(½ x) + 6(⅓ x) = 6×5 → 3x + 2x = 30 → 5x = 30 → x = 6。始终检查解是否使任何分母为零。
8. Checking Your Solution | 检验你的解
) + 1 = 9, which equals the right side. This habit catches mistakes and builds confidence.
将你的答案代回原方程进行验证。如果两边相等，你的解就是正确的。例如，对于 2x + 1 = 9，若 x = 4，则左边 = 2(4) + 1 = 9，等于右边。这个习惯能找出错误并树立信心。
9. Forming Equations from Word Problems | 从文字题建立方程
Translate phrases into algebraic expressions. "Three more than a number" becomes x + 3; "twice a number decreased by 5" becomes 2x − 5. Set up an equation using the relationship given. Example: "I think of a number, double it, add 7, and the result is 19." Equation: 2x + 7 = 19. Solve: 2x = 12, x = 6.
将短语翻译成代数表达式。“比一个数大3” 变成 x + 3；“一个数的两倍减去5” 变为 2x − 5。利用给定的关系建立方程。示例：“我想一个数，将它加倍，加7，结果是19。” 方程：2x + 7 = 19。求解：2x = 12，x = 6。
10. Common Mistakes and How to Avoid Them | 常见错误及其避免方法
negative sign precedes a bracket, multiply all terms inside by −1, e.g., −(x−2) = −x + 2.
常见错误包括忘记对两边进行相同运算、括号展开错误（如 3(x+4) = 3x+4）、或负号使用不当。要工整地写出每一步，使用天平法，并检验答案。当括号前有负号时，将括号内所有项乘以 −1，如 −(x−2) = −x + 2。
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