📚 Solving Equations with Variables on Both Sides | 解两边带变量的方程
In KS3 mathematics, solving equations where the unknown appears on both sides of the equals sign is a key skill. This article explains techniques, step-by-step examples, and common pitfalls.
在 KS3 数学中，解未知数出现在等号两边的方程是一项关键技能。本文讲解相关技巧、逐步示例和常见误区。
Mastering these will prepare you for more advanced topics such as inequalities and simultaneous equations.
掌握这些知识将为你学习不等式和联立方程组等更高级的主题做好准备。
1. What Are Equations with Variables on Both Sides? | 什么是两边带变量的方程？
riable x on both the left and right sides. This is common in algebra and requires specific techniques to solve.
诸如 2x + 5 = 3x − 2 这样的方程，变量 x 同时出现在左边和右边。这在代数中很常见，需要特定的方法来求解。
Unlike simple one-step equations, you cannot just divide or subtract in one move. You must reorganise the equation so that all variable terms appear on one side.
与简单的一步方程不同，你不能只通过一次除法或减法来解决。你必须重新整理方程，使所有变量项都出现在同一边。
In KS3, you will meet equations with the unknown on both sides in contexts such as perimeters, ages, and even simple financial problems.
在 KS3 中，你会在周长、年龄甚至简单的财务问题中遇到两边都含有未知数的方程。
2. The Balance Method: Keeping It Equal | 平衡法：保持等式平衡
Think of an equation as a balance scale. The left side must always equal the right side. Any operation applied to one side must also be applied to the other.
可以把方程想象成一个天平秤。左边必须始终等于右边。对一边进行的任何运算，也必须同时对另一边进行。
If you add 3 to the left, add 3 to the right. If you divide the left by 2, divide the right by 2. This principle ensures the equation stays true.
如果你在左边加上 3，右边也要加上 3。如果你将左边除以 2，右边也要除以 2。这个原则确保了方程始终成立。
Golden Rule: Do the same to both sides.
黄金法则：对等式两边做相同的运算。
Inverse operations help you strip away numbers and coefficients from the variable. The table below shows common pairs.
逆运算帮助你从变量身上剥离数字和系数。下表展示了常见的运算对。
| Operation | Inverse Operation |
|---|---|
| Addition (+) | Subtraction (−) |
| Subtraction (−) | Addition (+) |
| Multiplication (×) | Division (÷) |
| Division (÷) | Multiplication (×) |
Always apply the inverse operation to both sides. This logical approach prevents errors and builds confidence.
始终将逆运算应用于等式两边。这种合乎逻辑的方法可以防止错误并建立信心。
3. Simplifying Expressions First | 首先简化表达式
Before moving terms, simplify each side of the equation if possible. Combine like terms and expand brackets. This makes the equation cleaner and reduces mistakes.
在移项之前，如果可能的话，先化简等式的每一边。合并同类项，展开括号。这会使方程更清晰并减少错误。
d the bracket on the left: 6x − 2 + 4 = 6x + 2. Then the equation becomes 6x + 2 = 5x + 3.
例如：2(3x − 1) + 4 = 5x + 3。展开左边的括号：6x − 2 + 4 = 6x + 2。那么方程变为 6x + 2 = 5x + 3。
Remember to multiply each term inside the brackets carefully. A typical error is to write 2(3x − 1) as 6x − 1, forgetting to multiply the −1 by 2.
记住要小心地将括号内的每一项都乘上系数。一个典型错误是将 2(3x − 1) 写成 6x − 1，而忘记将 −1 乘以 2。
Also, collect constant terms on each side: 4 + (−2) becomes 2, not −6. Simplifying first often reveals a much easier
Published by TutorHao | KS3 Mathematics Revision Series | aleveler.com
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