Solving Linear Equations with Unknowns on Both Sides | 解一元一次方程：未知数在等号两边

📚 Solving Linear Equations with Unknowns on Both Sides | 解一元一次方程：未知数在等号两边

Linear equations are at the heart of KS3 algebra. They describe relationships where one unknown number must be found. This article explains how to solve equations such as 5x + 2 = 3x + 10, where the unknown x appears on both sides. You will learn a step-by-step method that works for brackets, fractions and negative terms.

线性方程是 KS3 代数的核心。它们描述必须求出一个未知数的关系。本文讲解如何求解像 5x + 2 = 3x + 10 这样未知数 x 出现在等号两边的方程。你将学会一种分步方法，适用于括号、分数和负项。

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1. What is a linear equation? | 什么是线性方程？

A linear equation is an equation in which the unknown appears only to the power 1. There are no terms such as x², x³, 1/x or xy.

线性方程是未知数只出现一次幂的方程。没有 x²、x³、1/x 或 xy 这样的项。

The standard form we meet at KS3 is ax + b = cx + d, where a, b, c and d are numbers. Solving means finding the value of x that makes both sides equal.

我们在 KS3 遇到的标准形式是 ax + b = cx + d，其中 a、b、c、d 是数字。解方程就是求出使两边相等的 x 值。

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2. The balance method | 天平法

An equation behaves like a balanced scale. If you add, subtract, multiply or divide one side, you must do exactly the same to the other side.

方程就像一个平衡的天平。如果你对一边加、减、乘或除以某个数，你必须对另一边做完全相同的操作。

This rule keeps the equation true while you change its appearance. The goal is to transform the equation into the simple form x = a number.

这条规则在你改变方程外观时保持等式成立。目标是把方程变成 x = 一个数 的简单形式。

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3. Simplify each side first | 先化简等号两边

Before moving terms, simplify each side separately. Collect all like terms on the left and all like terms on the right.

在移项之前，先分别化简等号两边。合并左边和右边的所有同类项。

For example, 2x + 3 + x = 4x − 5 simplifies to 3x + 3 = 4x − 5.

例如，2x + 3 + x = 4x − 5 化简为 3x + 3 = 4x − 5。

2x + 3 + x = 4x − 5 → 3x + 3 = 4x − 5

Simplifying reduces mistakes and makes the next step clearer.

化简可以减少错误，并使下一步更清晰。

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4. Remove the smaller unknown term | 去掉较小的未知数项

When x appears on both sides, remove the smaller x term first. This keeps the coefficient of x positive and avoids negative sign errors.

当 x 出现在等号两边时，先去掉较小的 x 项。这样可以使 x 的系数为正，避免负数符号错误。

For 5x + 2 = 3x + 10, subtract 3x from both sides.

对于 5x + 2 = 3x + 10，两边同时减去 3x。

5x + 2 − 3x = 3x + 10 − 3x → 2x + 2 = 10

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5. Isolating the unknown | 分离未知数

Now that the unknown is on one side, use inverse operations. Undo addition or subtraction first, then undo multiplication or division.

现在未知数已经在一边，使用逆运算。先处理加法或减法，再处理乘法或除法。

From 2x + 2 = 10, subtract 2 from both sides to get 2x = 8. Then divide both sides by 2 to get x = 4.

从 2x + 2 = 10 开始，两边减去 2，得到 2x = 8。然后两边除以 2，得到 x = 4。

2x + 2 = 10 → 2x = 8 → x = 4

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6. Equations with brackets | 含括号的方程

If brackets are present, expand them first using a(b + c) = ab + ac. Then collect like terms and solve.

如果有括号，先用 a(b + c) = ab + ac 展开。然后

Published by TutorHao | KS3 Mathematics Revision Series | aleveler.com

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