📚 Solving Linear Equations with Unknowns on Both Sides | 解一元一次方程：未知数在等号两边
here 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。
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。
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。
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。
e 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。
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。
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
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。
= 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
6. Equations with brackets | 含括号的方程
re 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
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