Simple Linear Equations

🎯 Learning Objectives

By the end of this lesson, students should be able to:

• Understand the meaning of linear equations.
• Identify variables, constants, coefficients, and equality signs.
• Solve simple linear equations in one variable.
• Apply inverse operations to find unknown values.
• Form and solve equations from real-life situations.

🧮 Lesson Introduction

An equation is a mathematical statement that shows two expressions are equal.
A linear equation is one in which the highest power of the variable is 1.
Linear equations are called one-step, two-step, or multi-step depending on how many operations are required to solve them.

The goal in solving an equation is to find the value of the unknown variable that makes the equation true.

🧠 Key Concepts

1️⃣ Basic Terms

2️⃣ Solving Linear Equations (One Step)

To solve, perform the inverse operation on both sides of the equation.

Example 1:
( x + 5 = 12 )
Subtract 5 from both sides → ( x = 12 – 5 )
✅ ( x = 7 )

Example 2:
( 3x = 12 )
Divide both sides by 3 → ( x = 12 ÷ 3 )
✅ ( x = 4 )

3️⃣ Two-Step Linear Equations

These require two operations — usually addition/subtraction and multiplication/division.

Example 1:
( 2x + 3 = 11 )
Subtract 3 → ( 2x = 8 )
Divide by 2 → ( x = 4 )

Example 2:
( 5x – 4 = 21 )
Add 4 → ( 5x = 25 )
Divide by 5 → ( x = 5 )

4️⃣ Equations with Brackets

Expand the brackets first, then solve.

Example:
( 3(x – 2) = 9 )
Expand → ( 3x – 6 = 9 )
Add 6 → ( 3x = 15 )
Divide by 3 → ( x = 5 )

5️⃣ Equations with Variables on Both Sides

Move the smaller variable to one side to make solving easier.

Example:
( 4x + 3 = 2x + 9 )
Subtract ( 2x ) from both sides → ( 2x + 3 = 9 )
Subtract 3 → ( 2x = 6 )
Divide by 2 → ( x = 3 )

6️⃣ Forming Linear Equations from Word Problems

Example:
The sum of twice a number and 5 gives 13. Find the number.

Let the number be ( x ).
Equation: ( 2x + 5 = 13 )
Subtract 5 → ( 2x = 8 )
Divide by 2 → ( x = 4 )

✅ The number is 4.

⚠️ Common Mistakes

• Forgetting to perform the same operation on both sides.
• Dropping the negative sign when moving terms.
• Misinterpreting “the sum of”, “difference between”, or “twice” in word problems.

🧩 Classroom Practice

Solve the following:

1. ( x + 7 = 15 )
2. ( 4x = 20 )
3. ( 2x + 3 = 11 )
4. ( 5x – 6 = 19 )
5. ( 3(x – 1) = 9 )