📚 Mastering Linear Equations: From Balancing to Solving | 掌握线性方程：从等式平衡到求解
In KS3 Cambridge Mathematics, linear equations form a central part of algebra. They allow students to model real-world problems and develop logical reasoning. This article explains how to solve linear equations step by step, from simple one-step cases to equations with fractions and brackets.
在 KS3 剑桥数学中，线性方程是代数的核心内容。它们帮助学生建立现实问题的数学模型并培养逻辑推理能力。本文逐步讲解如何求解线性方程，从简单的一步方程到含分数和括号的方程。
1. What is a Linear Equation? | 什么是线性方程？
to the first power. For example, 2x + 3 = 11 is linear because x is not squared or cubed.
线性方程是指未知数只出现一次方的方程。例如 2x + 3 = 11 是线性方程，因为 x 没有平方或立方。
ion in one variable is ax + b = c, where a, b and c are known values and x is the unknown.
一元线性方程的一般形式是 ax + b = c，其中 a、b、c 是已知数，x 是未知数。
To identify a linear equation, check that the variable has no exponent other than 1. Expressions such as x² or x³ are not linear.
要识别线性方程，请检查变量的指数是否为 1。像 x² 或 x³ 这样的表达式不是线性的。
3x - 4 = 14
2. The Balance Method | 等式平衡法
Think of an equation as a balance scale. The left side and the right side must always have the same value.
可以把方程想象成一个天平。左边和右边的值必须始终相等。
Whatever operation you do to one side, you must do exactly the same to the other side. This keeps the equation balanced while isolating the unknown.
无论对方程的一边进行什么运算，都必须对另一边做完全相同的运算。这样在隔离未知数的同时保持方程平衡。
If we have x + 5 = 12, subtracting 5 from both sides gives x = 7.
如果我们有 x + 5 = 12，两边同时减去 5，得到 x = 7。
x + 5 = 12
x = 12 - 5
x = 7
3. Inverse Operations | 逆运算
Inverse operations undo each other. Addition and subtraction are inverse operations, and multiplication and division are inverse operations.
逆运算可以相互抵消。加法和减法互为逆运算，乘法和除法互为逆运算。
To solve an equation, use the inverse operation to remove a number from the side containing the variable.
解方程时，使用逆运算将数字从含有变量的一边移走。
| Operation in equation | Inverse operation |
| + 4 | - 4 |
| - 6 | + 6 |
| × 3 | ÷ 3 |
| ÷ 5 | × 5 |
Always apply the inverse operation to both sides, not just one side.
务必对两边同时使用逆运算，而不是只对一边使用。
4. Solving One-Step Equations | 解一步方程
For x + 7 = 15, subtract 7 from both sides to get x = 8.
对于 x + 7 = 15，两边同时减去 7，得到 x = 8。
x + 7 = 15
x = 15 - 7
x = 8
For x - 4 = 10, add 4 to both sides to get x = 14.
对于 x - 4 = 10，两边同时加上 4，得到 x = 14。
x - 4 = 10
x = 10 + 4
x = 14
For 5x = 35, divide both sides by 5 to get x = 7.
对于 5x = 35，两边同时除以 5，得到 x = 7。
