Solving Linear Equations | 解一元一次方程

📚 Solving Linear Equations | 解一元一次方程

A linear equation is one of the most important tools in KS3 mathematics. It describes a relationship where the unknown value, usually written as x or n, is raised only to the power of 1. Learning to solve linear equations builds the foundation for algebra, graphs, and real-world problem solving.

一元一次方程是 KS3 数学中最重要的工具之一。它描述的是未知数（通常写作 x 或 n）的次数仅为 1 的关系。学会解一元一次方程将为代数、图像以及实际问题的解决打下基础。

1. What is a Linear Equation? | 什么是一元一次方程？

A linear equation is an equation of the form ax + b = c, where a, b and c are numbers and x is the unknown. The word ‘linear’ means that the variable appears only to the first power, so there is no x², x³ or 1/x term. For example, 2x + 3 = 11 is linear, but x² + 3 = 11 is not.

一元一次方程是形如 ax + b = c 的方程，其中 a、b、c 是数字，x 是未知数。’一次’ 指的是变量只出现一次方，因此没有 x²、x³ 或 1/x 这样的项。例如 2x + 3 = 11 是一次方程，而 x² + 3 = 11 不是。

In KS3, you will usually meet equations such as x + 5 = 12, 4x = 20, 2x + 3 = 7, and 5x − 2 = 3x + 6. The goal is always the same: find the number that makes the equation true.

在 KS3 阶段，你通常会遇到形如 x + 5 = 12、4x = 20、2x + 3 = 7 和 5x − 2 = 3x + 6 的方程。目标始终相同：找到使方程成立的数。

2. The Balance Method | 等式平衡法

Equations behave like a balanced set of scales. Whatever you do to one side, you must do to the other side to keep the scales balanced. This is called the balance method, and it is the golden rule for solving equations.

方程就像一个平衡的天平。你对一边做什么操作，就必须对另一边做同样的操作，才能保持天平平衡。这叫做等式平衡法，它是解方程的黄金法则。

If you add 5 to the left-hand side, you must add 5 to the right-hand side. If you divide the left-hand side by 3, you must divide the right-hand side by 3. This keeps the equation equivalent to the original one.

如果你在左边加 5，就必须在右边也加 5。如果你把左边除以 3，就必须把右边也除以 3。这样方程才会和原来的方程等价。

Using the balance method correctly means that the equals sign stays true at every step. You can think of the equals sign as the centre of the balance.

正确使用平衡法意味着等号在每一步都保持成立。你可以把等号想象成天平的中心。

3. Solving One-Step Equations | 解一步方程

Some equations only need one operation to solve. For example, x + 5 = 12. To isolate x, subtract 5 from both sides: x + 5 − 5 = 12 − 5, so x = 7.

有些方程只需要一步运算就能求解。例如 x + 5 = 12。为了单独得到 x，两边同时减去 5：x + 5 − 5 = 12 − 5，所以 x = 7。

If the equation is 4x = 20, divide both sides by 4: 4x ÷ 4 = 20 ÷ 4, so x = 5. If the equation is x ÷ 3 = 6, multiply both sides by 3: (x ÷ 3) × 3 = 6 × 3, so x = 18.

如果方程是 4x = 20，两边同时除以 4：4x ÷ 4 = 20 ÷ 4，所以 x = 5。如果方程是 x ÷ 3 = 6，两边同时乘以 3：(x ÷ 3) × 3 = 6 × 3，所以 x = 18。

Remember that addition and subtraction are inverse operations, and multiplication and division are inverse operations. Choosing the inverse operation helps you get the unknown on its own.

记住加法和减法互为逆运算，乘法和除法也互为逆运算。选择逆运算可以帮助你把未知数单独留在一边。

4. Solving Two-Step Equations | 解两步方程

Many KS3 equations require two steps. For example, 2x + 3 = 11. First subtract 3 from both sides to get 2x = 8. Then divide both sides by 2 to get x = 4.

许多 KS3 方程需要两步求解。例如 2x + 3 = 11。首先

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