CHAPTER

Simple Equations in One Variable

5.1 Simple Linear Equations in One Variable · 平衡法解方程 5.2 Linear Equations Involving Brackets and Fractions · 括号 / 分数方程 5.3 Simple Fractional Equations · 变量在分母的方程 5.4 Formulate Linear Equations to Solve Word Problems · 用方程解应用题 ★ 章末：Sum Up · Review Exercise 5 · Problem Solving Task · Maths Journal

A party planner is planning a birthday event for his client. To propose a budget, he needs to know the cost of the food, the rental cost of the venue and the number of guests attending.

The cost of food for each guest is $30 and renting the venue costs $800. If the client's budget is $1400, how many guests can attend the party?

Can we just guess? Or is there a faster way?

Let n = number of guests. Then total cost = 30n + 800. Setting this equal to the budget gives the equation:

30n + 800 = 1400

Solving: subtract 800 → 30n = 600; divide by 30 → n = 20.
20 guests can attend. This is the power of an equation: it lets us solve for an unknown instead of guessing.

In Chapter 4 we wrote algebraic expressions (no equal sign). In this chapter we introduce the equal sign — turning expressions into equations. We then learn the rules to systematically solve for the unknown variable.

📚 本章学习目标 · Learning objectives

Make sense of the concept of an equation
Solve linear equations in one variable using the balance method (add / subtract / multiply / divide both sides)
Solve simple fractional equations that can be reduced to linear equations
Formulate linear equations in one variable to solve word problems

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