Solving Linear Equations: Balanced Methods for KS3 | 解一元一次方程：KS3 平衡法与技巧

📚 Solving Linear Equations: Balanced Methods for KS3 | 解一元一次方程：KS3 平衡法与技巧

Linear equations are one of the most important building blocks of KS3 Cambridge mathematics. They appear in algebra, number problems, geometry and real-life contexts, so being able to solve them confidently is essential for progress.

一元一次方程是 KS3 剑桥数学最重要的基础模块之一。它们出现在代数、数论问题、几何和实际情境中，因此能够熟练解方程对于后续学习至关重要。

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

A linear equation is an algebraic statement where two expressions are set equal to each other, and the unknown letter, usually x, is only raised to the power 1. For example, 2x + 3 = 11 is a linear equation because the highest power of x is 1.

一元一次方程是将两个代数式用等号连接起来的等式，其中未知数字母通常为 x，并且 x 的最高次数为 1。例如 2x + 3 = 11 是一元一次方程，因为 x 的最高次数是 1。

An equation is different from an expression. An expression such as 3x + 5 does not have an equals sign, while an equation such as 3x + 5 = 20 states that two things are equal.

方程与表达式不同。像 3x + 5 这样的表达式没有等号，而像 3x + 5 = 20 这样的方程则说明两个量相等。

The solution of a linear equation is the value of x that makes the equation true. Solving means finding that value systematically rather than guessing.

一元一次方程的解就是使等式成立的 x 的值。解方程是指用系统的方法求出这个值，而不是靠猜测。

2x + 3 = 11 ⇒ x = 4

2. The Balance Method | 平衡法

Think of an equation as a balanced set of scales. The left-hand side and the right-hand side must always stay equal, so whatever you do to one side, you must do to the other side.

把方程想象成一台平衡的天平。左边和右边必须始终保持相等，所以对一边做什么运算，对另一边也要做相同的运算。

If you add the same number to both sides, subtract the same number, multiply both sides by the same non-zero number, or divide both sides by the same non-zero number, the equality is preserved.

如果两边同时加上同一个数、同时减去同一个数、同时乘以同一个非零数或同时除以同一个非零数，等式仍然成立。

The balance method is the foundation of all equation solving at KS3 and Cambridge Checkpoint level. It helps you keep the equation true while you rearrange it into the form x = a.

平衡法是 KS3 和剑桥 Checkpoint 阶段解所有方程的基础。它能帮助你在逐步变形为 x = a 的形式时保持等式始终成立。

3. Solving One-Step Equations | 解一步方程

Some equations only need one operation to isolate x. For x + 5 = 12, 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出 x。对于 x + 5 = 12，两边同时减去 5：x + 5 – 5 = 12 – 5，所以 x = 7。

For x – 7 = 3, add 7 to both sides: x – 7 + 7 = 3 + 7, giving x = 10.

对于 x – 7 = 3，两边同时加上 7：x – 7 + 7 = 3 + 7，得到 x = 10。

For 3x = 18, divide both sides by 3: 3x ÷ 3 = 18 ÷ 3, so x = 6.

对于 3x = 18，两边同时除以 3：3x ÷ 3 = 18 ÷ 3，所以 x = 6。

For x ÷ 4 = 9, multiply both sides by 4: x ÷ 4 × 4 = 9 × 4, so x = 36.

对于 x ÷ 4 = 9，两边同时乘以 4：x ÷ 4 × 4 = 9 × 4，所以 x = 36。

A quick table can help you remember the inverse operation you need for each type of one-step equation.

下面的表格可以帮助你记住每种一步方程所需的逆运算。

4. Solving Two-Step Equations | 解两步方程

A two-step equation involves two operations, such as 2x + 3 = 11. First undo the addition by subtracting 3 from both sides: 2x = 8. Then undo the multiplication by dividing both sides by 2: x = 4.

两步方程包含两种运算，例如 2x +

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