📚 Solving Linear Equations for KS3 Cambridge Maths | KS3剑桥数学：解一元一次方程
At KS3 Cambridge Mathematics, solving linear equations is a key algebraic skill. You learn how to find the value of an unknown letter, usually x or y, by using inverse operations and keeping an equation balanced. This guide walks through the essential methods, written examples and common exam-style tips for Cambridge Lower Secondary learners.
在KS3剑桥数学中，解一元一次方程是一项核心代数技能。你将学习如何利用逆运算并保持等式平衡，求未知字母（通常是x或y）的值。本指南为剑桥初中阶段学生梳理关键方法、书写示例和常见考试技巧。
1. What Is a Linear Equation? | 什么是线性方程
power of 1. For example, 2x + 3 = 11 is linear because x is not squared or cubed. The word 'linear' tells you that the graph of the equation is a straight line.
线性方程是指未知数的次数仅为1的方程。例如，2x + 3 = 11 是线性的，因为 x 没有平方或立方。'线性'一词表示该方程的图像是一条直线。
he equation true. In 2x + 3 = 11, if x = 4, then 2 × 4 + 3 = 11, so the solution is x = 4.
方程的解是使等式成立的未知数的值。在 2x + 3 = 11 中，如果 x = 4，那么 2 × 4 + 3 = 11，因此解为 x = 4。
2. The Balance Method | 天平法（等式性质）
Think of an equation as a balance scale. The equals sign means both sides have the same value. Whatever you do to one side, you must do to the other side to keep the balance.
把方程想象成一台天平。等号意味着两边数值相等。你对一边做的任何运算，都必须对另一边做同样的运算，以保持平衡。
The key operations are: add or subtract the same number on both sides, multiply both sides by the same non-zero number, and divide both sides by the same non-zero number.
关键运算是：两边同时加或减同一个数；两边同时乘以同一个非零数；两边同时除以同一个非零数。
Always write your working vertically, keeping the equals signs lined up. This shows the examiner that you have used balance correctly.
书写时始终竖向排列，保持等号对齐。这能让阅卷老师看出你正确使用了等式平衡。
3. One-Step Equations | 一步方程
. For example, solve x + 5 = 12. Subtract 5 from both sides: x + 5 − 5 = 12 − 5, so x = 7.
一步方程只需进行一次逆运算。例如，解 x + 5 = 12。两边同时减去5：x + 5 − 5 = 12 − 5，所以 x = 7。
If the equation is 3x = 18, divide both sides by 3: 3x ÷ 3 = 18 ÷ 3, so x = 6.
如果方程是 3x = 18，两边同时除以3：3x ÷ 3 = 18 ÷ 3，所以 x = 6。
nator, such as 20 ÷ x = 5, multiply both sides by x first, then divide: 20 = 5x, so x = 4.
如果未知数在分母中，例如 20 ÷ x = 5，先两边乘以 x，再除以：20 = 5x，所以 x = 4。
4. Two-Step Equations | 两步方程
th sides to get 2x = 8. Then undo the multiplication: divide both sides by 2 to get x = 4.
两步方程包含两种运算。例如，解 2x + 3 = 11。先消去加法：两边同时减去3，得到 2x = 8。再消去乘法：两边同时除以2，得到 x = 4。
Remember to reverse the order of operations. Undo adding/subtracting before multiplying/dividing, because in the original expression multiplication happens before addition.
记住要逆用运算顺序。先消去加减法，再消去乘除法，因为原表达式中乘法先于加法。
Example: solve 7x − 9 = 26. Add 9 to both sides: 7x = 35. Then divide by 7: x = 5.
例如：解 7x − 9 = 26。两边加9：7x = 35。然后除以7：x = 5。
5. Equations with Brackets | 带括号的方程
example, 3(x + 2) = 21. Expand: 3x + 6 = 21. Then subtract 6: 3x = 15. Divide by 3: x = 5.
如果方程含有括号，先利用乘法分配律展开。例如，3(x + 2) = 21。展开：3x + 6 = 21。然后减去6：3x = 15。除以3：x = 5。
3(x + 2) = 21, divide both sides by 3 to get x + 2 = 7, then x = 5. This is often quicker.
如果因数能整除，也可以先两边除以这个因数。在 3(x + 2) = 21 中，两边除以3得到 x + 2 = 7，所以 x = 5。这通常更快捷。
Be careful with negative brackets: −2(x − 4) = 10 expands to −2x + 8 = 10, not −2x − 8.
注意负号括号：−2(x − 4) = 10 展开为 −2x + 8 = 10，而不是 −2x − 8。
6. Unknowns on Both Sides | 两边都有未知数
rms on one side and numbers on the other. For example, solve 5x + 2 = 2x + 11. Subtract 2x
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