7C Homework Answers: Solving Linear Equations | 7C 作业答案：解一元一次方程

📚 7C Homework Answers: Solving Linear Equations | 7C 作业答案：解一元一次方程

This article provides worked solutions for Exercise 7C, which focuses on solving one-step and two-step linear equations. Each answer is explained step by step so you can check your homework and understand the method.

本文提供练习 7C 的详细解答，该练习重点是一元一次方程的一步和两步求解。每个答案都逐步解释，方便你核对作业并理解解题方法。

1. General Strategy for Solving Linear Equations | 解一元一次方程的总体策略

To solve any linear equation, aim to isolate the variable on one side of the equation. Use inverse operations: addition and subtraction undo each other, and multiplication and division undo each other.

解任何一元一次方程，目标都是将变量单独留在方程的一边。使用逆运算：加法和减法互相抵消，乘法和除法互相抵消。

Always keep the equation balanced by performing the same operation on both sides. Check your final answer by substituting it back into the original equation.

始终对方程两边执行相同的运算，以保持方程平衡。最后把答案代回原方程进行检验。

The core skills tested in 7C include expanding brackets, collecting like terms, and handling fractional or decimal coefficients.

7C 考查的核心技能包括去括号、合并同类项，以及处理分数或小数系数。

2. Solve 3x + 5 = 20 | 第2题：解 3x + 5 = 20

Subtract 5 from both sides: 3x + 5 − 5 = 20 − 5, giving 3x = 15.

两边同时减去 5：3x + 5 − 5 = 20 − 5，得到 3x = 15。

Divide both sides by 3: 3x ÷ 3 = 15 ÷ 3, hence x = 5.

两边同时除以 3：3x ÷ 3 = 15 ÷ 3，因此 x = 5。

Answer: x = 5. Check: 3(5) + 5 = 15 + 5 = 20.

答案：x = 5。 检验：3(5) + 5 = 15 + 5 = 20。

Common mistake: some students divide by 3 before subtracting 5. This gives x + 5 ≈ 6.67, which is incorrect because addition and subtraction must be undone before multiplication and division.

常见错误：有些学生先除以 3，而不是先减去 5。这样会得到 x + 5 ≈ 6.67，这是错误的，因为必须先处理加减，再处理乘除。

3. Solve 2(x − 3) = 8 | 第3题：解 2(x − 3) = 8

First expand the bracket on the left: 2(x − 3) means 2 × x − 2 × 3, so 2x − 6 = 8.

首先展开左边的括号：2(x − 3) 表示 2 × x − 2 × 3，所以 2x − 6 = 8。

Add 6 to both sides: 2x − 6 + 6 = 8 + 6, so 2x = 14.

两边同时加上 6：2x − 6 + 6 = 8 + 6，得到 2x = 14。

Divide both sides by 2: 2x ÷ 2 = 14 ÷ 2, hence x = 7.

两边同时除以 2：2x ÷ 2 = 14 ÷ 2，因此 x = 7。

Answer: x = 7. Check: 2(7 − 3) = 2 × 4 = 8.

答案：x = 7。 检验：2(7 − 3) = 2 × 4 = 8。

Common mistake: forgetting to multiply both terms inside the bracket by 2

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