Lesson 4: Solving Linear Equations in One Variable

👨🏽‍🏫 Introduction

Let’s say you’re buying snacks 🍫. You get two meat pies and a drink, and the total bill is ₵10. If the drink costs ₵4, how much is one meat pie?

Let’s use algebra: If one meat pie costs ₵x, then the total is . Solving this equation gives you the value of x — that’s the goal of this lesson!

By the end of this lesson, you’ll be able to:

• Understand what a linear equation is
• Apply rules to isolate the unknown (variable)
• Solve real-life problems by forming and solving equations

🧠 Key Concepts

📌 1. What Is a Linear Equation?

A linear equation in one variable is an equation that:

• Has only one variable (like x)
• Has no powers (no or )
• Forms a straight line when graphed

Examples:

🔑 2. Solving Linear Equations: The Goal

The goal is to find the value of x that makes the equation true. This is called “solving for x”.

We do this by performing the same operation on both sides of the equation to keep it balanced — just like a scale ⚖️.

🛠️ 3. Common Solving Techniques

1. Remove brackets using expansion
2. Collect like terms on each side
3. Move all terms with the variable to one side
4. Move constants to the other side
5. Divide or multiply to isolate the variable

🧮 Sample Problem Walkthroughs

1. Solve:
   Step 1: Subtract 3 from both sides:
   
2. Solve:
   Step 1: Add 4 to both sides →
   Step 2: Divide both sides by 2 →
3. Solve:
   Step 1: Expand brackets →
   Step 2: Add 6 →
   Step 3: Divide by 3 →
4. Solve:
   Step 1: Subtract 2 →
   Step 2: Multiply both sides by 3 →
5. Solve:
   Step 1: Move all x terms to one side →
   Step 2: Simplify →
   Step 3: Divide by 2 →

✍🏽 Practice Exercises

🅰️ A. Solve the following equations:

✅ Answers and Explanations

• A1: Add 7 →
• A2: Subtract 3 → , then divide by 4 →
• A3: Expand → , then add 5 → →
• A4: Multiply both sides by 5 → → Divide by 2 →
• A5: Subtract x → → Add 2 → →

📌 Recap

• ✅ A linear equation has one variable and no exponents
• ✅ Use inverse operations to isolate the variable
• ✅ Keep both sides of the equation balanced by doing the same operation to both sides

💭 Reflection Prompt

Have you ever had to calculate how many items you can buy with a set amount of money? Try writing it as an equation, then solve it. For example: “If pens cost ₵2 each and you have ₵10, how many can you buy?” Let and solve!