Solving Linear Equations: KS3 Cambridge Maths | 解一元一次方程：KS3剑桥数学

📚 Solving Linear Equations: KS3 Cambridge Maths | 解一元一次方程：KS3剑桥数学

Linear equations are the foundation of algebra at KS3. On page 140 of the Cambridge Checkpoint Maths series, you will meet equations such as x + 3 = 7, 4x = 20 and 2(x – 1) = x + 5. Mastering these skills allows you to solve problems in geometry, science and everyday life. This article explains the key methods step by step and gives you the confidence to tackle any Cambridge KS3 equation question.

线性方程是 KS3 代数的基础。在剑桥 Checkpoint 数学系列的第 140 页，你会遇到像 x + 3 = 7、4x = 20 和 2(x – 1) = x + 5 这样的方程。掌握这些技能能帮助你解决几何、科学和日常生活中的问题。本文逐步讲解核心方法，帮助你自信应对任何剑桥 KS3 方程题。

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

A linear equation is an equation in which the unknown, usually written as x, is raised only to the power of 1. This means there are no x² terms, no square roots of x, and no fractions where x appears in the denominator. For example, 3x + 5 = 14 is linear, but x² + 2 = 6 is not. The word ‘linear’ comes from the fact that the graph of y = 3x + 5 is a straight line.

线性方程是指未知数（通常写作 x）的指数只为 1 的方程。也就是说，方程中没有 x² 项，没有 x 的平方根，也没有 x 出现在分母中的分数。例如，3x + 5 = 14 是线性方程，但 x² + 2 = 6 不是。’线性’ 一词来源于 y = 3x + 5 的图像是一条直线。

In KS3, you solve linear equations by finding the value of x that makes the equation true. This value is called the solution or root. The equals sign acts like a balance: whatever you do to one side, you must do to the other side to keep the equation balanced.

在 KS3 阶段，你通过求出使方程成立的 x 值来解线性方程。这个值叫做方程的解或根。等号的作用就像一个天平：你对等式的一边做了什么，就必须对另一边做同样的操作，以保持方程平衡。

2. The Balance Method | 天平法

The balance method is the most reliable way to solve linear equations. Imagine each side of the equation is a pan on a balance scale. If you add, subtract, multiply or divide one side by a number, you must do exactly the same to the other side. This keeps the pans level and the equation true.

天平法是解线性方程最可靠的方法。把方程的两边想象成天平的两个托盘。如果你对一边进行加、减、乘或除以一个数，你必须对另一边做完全相同的操作。这样托盘才能保持水平，方程才成立。

For example, to solve x + 6 = 15, subtract 6 from both sides: x + 6 – 6 = 15 – 6, which simplifies to x = 9. You can check by substituting 9 back into the original equation: 9 + 6 = 15, so the solution is correct.

例如，解 x + 6 = 15，两边同时减去 6：x + 6 – 6 = 15 – 6，化简得 x = 9。你可以把 9 代回原方程检验：9 + 6 = 15，所以解是正确的。

Writing the operation on both sides on the same line, or directly below, helps you show method marks in Cambridge exams. Even when you can see the answer mentally, always show the balancing step.

把两边进行的操作写在同一行或正下方，有助于你在剑桥考试中拿到过程分。即使你能直接看出答案，也要写出平衡步骤。

3. Solving with Addition and Subtraction | 用加法与减法解方程

When a number is added to or subtracted from the unknown, undo that operation by using its inverse. If the equation says x – 4 = 10, add 4 to both sides: x – 4 + 4 = 10 + 4, giving x = 14. If the equation says x + 7 = 3, subtract 7 from both sides: x = 3 – 7 = -4.

当未知数被加上或减去一个数时，用逆运算来消去它。如果方程是 x – 4 = 10，两边都加 4：x – 4 + 4 = 10 + 4，得到 x = 14。如果方程是 x + 7 = 3，两边都减 7：x = 3 – 7 = -4。

Many KS3 students find negative solutions challenging. Remember that subtracting a larger number from a smaller one gives a negative result. Practise with examples such as x + 9 = 2 and x – 5 = -3 until you are comfortable moving between positive and negative values.

许多 KS3 学生对负数解感到困难。记住，用较小的数减去较大的数会得到负数。多练习像 x + 9 = 2 和 x – 5 = -3 这样的例子，直到你能熟练处理正负数之间的转换。

Always line up the equation vertically so that the added or subtracted number appears clearly on both sides. This reduces careless mistakes when the solution is negative.

始终把方程垂直排列，使两边加或减的数字清晰可见。这样在解为负数时能减少粗心错误。

4. Solving with Multiplication and Division | 用乘法与除法解方程

If the unknown is multiplied by a number, divide both sides by that coefficient. For example, 5x = 35 becomes 5x ÷ 5 = 35 ÷ 5, so x = 7. If x is divided by a number, multiply both sides by that denominator. For x/4 = 9, multiply both sides by 4: x = 36.

如果未知数乘以一个数，两边都除以这个系数。例如，5x = 35 变为 5x ÷ 5 = 35 ÷ 5，所以 x = 7。如果 x 除以一个数，两边都乘以这个分母。对于 x ÷ 4 = 9，两边都乘以 4：x = 36。

Be careful with negative coefficients: in -3x = 12, divide both sides by -3 to get x = -4. A common sign error is to write x = 4 because the negative sign is forgotten.

注意负系数：在 -3x = 12 中，两边都除以 -3，得到 x = -4。一个常见的符号错误是忘记负号而写成 x = 4。Published by TutorHao | KS3 Mathematics Revision Series | aleveler.com

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