Lesson 2: Linear Equations in One Variable – Solving Step-by-Step

🟦 Introduction

Welcome! In this lesson, we focus on how to solve simple algebraic equations where there is only one unknown variable. A linear equation is like a balance scale — whatever you do on one side, you must do on the other! Today, you’ll learn how to solve these equations step-by-step and build a strong foundation for tougher math problems later.

🧠 Key Concepts and Explanations

🔹 What is a Linear Equation in One Variable?

A linear equation in one variable is an equation that involves only one variable, and that variable has a power of 1.

Examples: 2x + 3 = 7, 5y – 8 = 2, 4p/3 = 6

🔹 Solving a Linear Equation

To solve a linear equation:

1. Isolate the variable on one side of the equation.
2. Use inverse operations (opposite of + is -, opposite of × is ÷) to move numbers across the equals sign.
3. Always keep the equation balanced by doing the same operation to both sides.

🔹 Important Tips

• When you add or subtract a number on one side, do the same on the other side.
• When you multiply or divide, apply it equally to both sides.
• Always check your answer by substituting it back into the original equation!

➡️ Sample Problem Walkthroughs

🔹 Example 1: Simple Addition

Solve: x + 5 = 12

Step 1: Subtract 5 from both sides:

Step 2: Simplify:

🔹 Example 2: Simple Subtraction

Solve: y – 3 = 10

Step 1: Add 3 to both sides:

Step 2: Simplify:

🔹 Example 3: Division

Solve: p/4 = 5

Step 1: Multiply both sides by 4:

Step 2: Simplify:

🔹 Example 4: Two Steps

Solve: 2x + 3 = 11

Step 1: Subtract 3 from both sides:

Step 2: Divide both sides by 2:

📝 Practice Exercises

Practice 1: Solve the following

1. x + 8 = 15
2. y – 5 = 9
3. m/3 = 6
4. 4a – 7 = 9

Practice 2: Word Problem Challenge

A book costs GHC x. If you add GHC 5 more, the total cost becomes GHC 20. Find x.

Practice 3: Mixed Problems

1. k/2 + 3 = 11
2. 5b – 6 = 19
3. 3n/4 = 9

🔁 Recap

Today, you learned how to solve linear equations step-by-step:

• Use opposite operations (addition, subtraction, multiplication, division).
• Keep both sides balanced!
• Always check your final answer by substituting back into the equation.

🪞 Reflection Prompt

Think about it: Why is it important to do the same thing to both sides of an equation when solving?