Solving One-Step Equations | 解一步方程

📚 Solving One-Step Equations | 解一步方程

In KS3 Cambridge Mathematics, solving one-step equations is a fundamental skill that builds your algebra muscles. You will learn to find the value of an unknown variable using inverse operations – the key to unlocking harder topics later on. Once you master these simple equations, you will feel confident tackling two-step equations, inequalities and even graph work.

在剑桥初中数学中，解一步方程是一项练好代数基本功的核心技能。你将学习如何使用逆运算找出未知变量的值——这是以后攻克更复杂内容的关键。一旦掌握了这些简单方程，你就会自信地面对两步方程、不等式甚至图像问题。

1. What Are Equations? | 什么是方程？

An equation is a mathematical sentence that states two expressions are equal. It always contains an equals sign ‘=’. Usually, a letter (called a variable) stands for the unknown number we need to find. For example, in the equation x + 3 = 7, the letter x represents the unknown.

方程是一种数学句子，说明两个表达式相等。它始终包含等号‘=’。通常，一个字母（称为变量）代表我们需要找出的未知数。例如，在方程 x + 3 = 7 中，字母 x 代表未知数。

It is important not to confuse an equation with an expression. An expression like 2x + 5 does not have an equals sign; it is not a statement of equality. An equation, however, has a left side and a right side that are perfectly balanced.

重要的是不要混淆方程与表达式。像 2x + 5 这样的表达式没有等号；它不是相等关系的陈述。然而，方程有一个左边和一个右边，它们完美地保持平衡。

2. The Balance Method | 天平法

To solve an equation, we use the balance method. Think of a traditional weighing scale: if you place a weight on one side, you must place an identical weight on the other side to keep it level. This is the golden rule of algebra – whatever you do to one side of the equation, you must also do to the other.

要解方程，我们使用天平法。想象一个传统天平：如果你在一侧放上一个砝码，就必须在另一侧放上完全相同的砝码以保持水平。这就是代数的黄金法则——对方程一边做什么，另一边也必须做同样的事情。

This method ensures the equation remains true. The operations we use to isolate the variable are called inverse operations. For example, the inverse of addition is subtraction; the inverse of multiplication is division.

这一方法能保证方程始终成立。我们用来隔离变量的运算称为逆运算。例如，加法的逆运算是减法；乘法的逆运算是除法。

3. Solving Equations of the Form x + a = b | 解 x + a = b 形式的方程

If an equation adds a number to the variable, like x + 6 = 9, you must perform the inverse operation – subtraction – on both sides. This cancels the added number and leaves x by itself.

如果一个方程在变量上加了一个数，比如 x + 6 = 9，你必须对方程两边执行逆运算——减法。这会抵消掉加上的数，让 x 单独留在一边。

The steps are shown clearly in the table below:

下表清晰地展示了求解步骤：

The solution is x = 3. You can always check by substituting 3 back into the original equation: 3 + 6 = 9, which is true. Remember to keep the equals signs aligned in your written work – it makes your reasoning easy to follow.

解是 x = 3。你总是可以把 3 代回原方程进行检验：3 + 6 = 9，这是正确的。记住在书写时对齐等号，这会让你的推理过程更容易理解。

4. Solving Equations of the Form x − a = b | 解 x − a = b 形式的方程

When a number is subtracted from the variable, the inverse operation is addition. For instance, solve x − 4 = 5 by adding 4 to both sides.

当一个数从变量上减去时，逆运算是加法。例如，通过两边加 4 来解 x − 4 = 5。