📚 Solving Linear Equations | 一元一次方程求解
Linear equations are the foundation of algebra at KS3 Cambridge level. This article explains how to solve one-variable linear equations step by step, from simple one-step problems to equations with brackets, fractions, and unknowns on both sides. You will also learn how to form equations from word problems and how to check your answers carefully.
一元一次方程是 KS3 剑桥数学代数的基础。本文逐步讲解如何求解一元一次方程，从简单的一步方程到含括号、分数和两边都有未知数的方程。你还将学习如何从文字题中建立方程，以及如何仔细检验答案。
1. What Is a Linear Equation? | 什么是一元一次方程？
or example, 2x + 3 = 11 is a linear equation because the highest power of x is 1. The word 'linear' comes from the fact that the graph of such an equation is always a straight line.
一元一次方程是指未知数仅以一次幂出现的方程。在 KS3 剑桥数学中，学生使用形如 ax + b = c 的方程，其中 a、b、c 是数字，x 是未知数。例如，2x + 3 = 11 是一元一次方程，因为 x 的最高次数是 1。“线性”一词来自这种方程的图像总是一条直线。
Solving a linear equation means finding the value of the unknown that makes the equation true. This value is called the solution or the root. Equations can be solved by using inverse operations and by keeping the equation balanced at all times.
解一元一次方程就是求出使方程成立的未知数的值。这个值叫做方程的解或根。解方程可以使用逆运算，并始终保持方程两边平衡。
2. Keeping the Equation Balanced | 保持方程平衡
The most important rule in solving equations is to keep the equation balanced. Think of an equation as a set of balance scales. If you add or subtract the same amount on both sides, the scales remain level. If you multiply or divide both sides by the same non-zero number, the scales still remain level.
解方程最重要的规则是保持方程两边平衡。把方程想象成一架天平。如果在两边同时加上或减去相同的量，天平仍然保持水平。如果在两边同时乘以或除以同一个非零数，天平仍然水平。
if a = b, then a + c = b + c
act 5 from both sides to keep the balance. Because the same operation is applied to both sides, the solution is not changed. This balance rule is the core of all algebraic equation solving.
例如，如果 x + 5 = 12，你可以在两边同时减去 5 来保持平衡。因为两边进行了相同的操作，方程的解不会改变。这一平衡规则是所有代数方程求解的核心。
3. One-Step Equations: Addition and Subtraction | 一步方程：加法与减法
se of adding 7 is subtracting 7. Subtract 7 from both sides: x + 7 − 7 = 15 − 7, so x = 8.
一步方程只需要一次逆运算就能求解。对于 x + 7 = 15 这样的方程，加 7 的逆运算是减 7。两边同时减去 7：x + 7 − 7 = 15 − 7，所以 x = 8。
= 9 + 6, so x = 15. Learning to spot the inverse operation quickly is a key skill at KS3.
如果方程是 x − 6 = 9，减 6 的逆运算是加 6。两边同时加 6：x − 6 + 6 = 9 + 6，所以 x = 15。快速找到逆运算是 KS3 的一项关键技能。
4. One-Step Equations: Multiplication and Division | 一步方程：乘法与除法
peration. For 4x = 20, divide both sides by 4: x = 20 ÷ 4, so x = 5. The notation 4x means '4 times x', so dividing by 4 isolates x.
当未知数乘以或除以一个数时，使用相反的运算。对于 4x = 20，两边同时除以 4：x = 20 ÷ 4，所以 x = 5。记号 4x 表示“4 乘 x”，因此除以 4 可以分离出 x。
oefficient (the number in front of x) is not zero, because dividing by zero is not allowed.
对于 x ÷ 3 = 7，两边同时乘以 3：x = 7 × 3，所以 x = 21。一定要检查系数（x 前面的数）不为零，因为除以零是不允许的。
5. Two-Step Equations | 两步方程
undo the addition: 3x = 15. Then divide both sides by 3 to undo the multiplication: x = 5.
两步
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