📚 Solving Linear Equations | 解一元一次方程
Linear equations are the foundation of algebra. In KS3 Mathematics, you learn how to solve simple equations where you need to find the value of an unknown, usually represented by a letter like x. An equation is like a balanced set of scales – whatever you do to one side, you must do to the other to keep the balance. This article will guide you through the essential skills for solving one‑step, two‑step and multi‑step linear equations, including those with brackets and fractions.
一元一次方程是代数的基石。在 KS3 数学中，你将学习如何求解简单的方程，即找出未知数（通常用字母如 x 表示）的值。方程就像一架平衡的天平——你对一边做的任何操作，都必须对另一边做，以保持平衡。本文将带你掌握解一元一次方程的基本技巧，包括一步方程、两步方程、多步方程，以及含有括号和分数的方程。
1. What is a Linear Equation? | 什么是一元一次方程？
highest power of the unknown is 1. For example, 2x + 5 = 11 is a linear equation. The word 'linear' the variable that makes the equation true. In KS3, you will mainly work with equations in one variable.
一元一次方程是指未知数的最高次数为 1 的方程。例如，2x + 5 = 11 就是一个一元一次方程。“一次”这个词来源于这种方程的图像是一条直线。未知数通常被称为变量，方程的解就是使等式成立的变量的值。在 KS3 阶段，你主要学习含有一个变量的方程。
2. The Balancing Method | 天平平衡法
Think of an equation as a pair of scales in perfect balance. The expressions on the left and right sides have the same value. To solve the equation, you perform the same operation on both sides to isolate the variable. You can add, subtract, multiply or divide, but you must do it to both sides to maintain the balance. This idea is the golden rule of equation solving.
把方程想象成一对完全平衡的天平。左边和右边的表达式具有相同的值。为了解方程，你需要对两边同时进行相同的运算，以分离出变量。你可以加、减、乘、除，但必须对两边同时操作以保持平衡。这个思路是解方程的金科玉律。
3. Solving One‑Step Equations | 解一步方程
One‑ ke x - 3 = 9, add 3 to both sides to find x = 12. The key is to use the inverse operation.
一步方程只需要一次运算就能求解。例如，x + 7 = 15。为了消除加法，两边同时减去 7：x = 8。另一个例子是 4x = 20，两边同时除以 4 得到 x = 5。如果方程涉及减法，如 x - 3 = 9，两边同时加 3 得出 x = 12。关键是使用逆运算。
4. Solving Two‑Step Equations | 解两步方程
Two‑ ith addition or subtraction first, then multiplication or division. This is the reverse of the order of operations (BIDMAS).
两步方程涉及两种运算。以 2x + 5 = 13 为例。首先，消除加法：两边同时减去 5，得到 2x = 8。然后消除乘法：两边同时除以 2，所以 x = 4。一般的顺序是先处理加减，再处理乘除。这恰好是运算顺序（BIDMAS）的逆过程。
5. Checking Your Solution | 检查你的解
previous example, put x = 4 into 2(4) + 5: that gives 8 + 5 = 13, which matches the right‑ cking prevents careless errors and builds confidence. It is a good habit to develop early.
始终把你的答案代回原方程进行验证。对于前面的例子，将 x = 4 代入 2(4) + 5：得到 8 + 5 = 13，与右边相等。如果不成立，说明你犯了错误。检查可以防止粗心所致的错误，并建立信心。这是值得尽早养成的好习惯。
6. Equations with Brackets | 含有括号的方程
comes 3x + 6 = 21 after multiplying each term inside the bracket by 3. Then solve as a two‑ then divide by 3, so x = 5. Always remove brackets before carrying out inverse operations.
当你看到括号时，首先用分配律展开。例如，3(x + 2) = 21，将括号内的每一项乘以 3 后得到 3x + 6 = 21。然后当作两步方程求解：减去 6 得到 3x = 15，再除以 3，所以 x = 5。在进行逆运算之前，一定要先去掉括号。
7. Equations with Fractions | 含有分数的方程
t: x + 2 = 15, then subtract 2 to find x = 13. Always treat the fraction bar as a division – its inverse is multiplication.
分数看起来可能棘手，但你可以通过将两边乘以分母来消除它。例如，(x/4) = 3：两边乘以 4 得到 x = 12。如果分数的分子有更多项，如 (x + 2)/3 = 5，先乘以 3：x + 2 = 15，然后减去 2 得出 x = 13。始终将分数线视为除法——它的逆运算是乘法。
8. Solving Equations with Variables on Both Sides | 解变量在等号两边的方程
all variable terms to one side and numbers to the other. Use inverse operations carefully.
有时变量出现在等号两边，如 5x + 2 = 3x + 10。首先把变量项集中到一边。两边同时减去 3x，得到 2x + 2 = 10。然后减去 2 得到 2x = 8，所以 x = 4。目标是将所有含变量的项移到一边，数字移到另一边。小心使用逆运算。
9. Dealing with Negative Coefficients | 处理负系数
3, then multiply by -1 to get x = -3. Always aim to finish with a positive variable term.
如果变量的系数为负，如 -x + 4 = 7，你可以在等号两边加上 x，使系数变为正。或者将整个方程乘以 -1。对于 -x + 4 = 7，减去 4 得到 -x = 3，然后乘以 -1 得到 x = -3。始终以得到正的变量项为目标。
10. Equations That Simplify First | 需要先化简的方程
5 or 3.4. Always tidy up by expanding brackets and collecting like terms before balancing.
有些方程在求解前需要化简。例如，2(x + 3) + 3x = 23。展开：2x + 6 + 3x = 23。然后合并同类项：5x + 6 = 23。再求解：减去 6 得到 5x = 17，所以 x = 17/5 或 3.4。在运用平衡法之前，总是要先通过展开括号和合并同类项来整理方程。
11. Common Mistakes to Avoid | 常见错误与避免方法
Many students forget to perform an operation on both sides. Others mishandle negative signs or incorrectly apply the distributive law. Remember that x + x equals 2x, not x². Also, when multiplying a bracket by a negative number like -2(x - 3), the result is -2x + 6, not -2x - 6. Careful step‑by‑step working is your best defence.
许多学生会忘记对等号两边同时进行操作。也有人处理不好负号或错误地应用分配律。记住 x + x 等于 2x，而不是 x²。另外，用负数乘括号时，如 -2(x - 3)，结果是 -2x + 6，而不是 -2x - 6。一步步仔细计算是最好的防范措施。
12. Practice Examples and Summary | 练习例题与总结
ions prepares you for topics like graphs, simultaneous equations and problem solving. Remember the golden rule: keep the equation balanced by doing the same to both sides. With consistent practice, solving linear equations becomes second nature.
尝试求解：4(y - 2) = 16；(2x + 4)/3 = 8；6x - 7 = 2x + 9。掌握一元一次方程将为你进一步学习图像、联立方程和解决问题等主题做好准备。记住黄金法则：对等号两边执行相同的操作以保持平衡。通过持续练习，解一元一次方程将成为你的第二天性。
Published by TutorHao | KS3 Mathematics Revision Series | aleveler.com
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