Solving Linear Equations Using Inverse Operations

What you’ll learn

In this lesson, you’ll learn how to solve linear equations by using inverse operations to isolate the variable.

Why this matters

Solving equations is the heart of algebra. It allows students to find unknown values and model real-life situations involving cost, distance, time, and more.

What is a linear equation?

A linear equation is an equation where the variable is raised only to the first power.

Example:

This equation means:

“A number plus 5 equals 12.”

Our goal is to find the value of x that makes the equation true.

Understanding equations as balance

Think of an equation like a balance scale.

• Both sides must stay equal

• Whatever you do to one side, you must do to the other

This idea guides every step of solving equations.

What are inverse operations?

Inverse operations undo each other.

Examples:

• Addition ↔ Subtraction

• Multiplication ↔ Division

We use inverse operations to undo what’s being done to the variable.

Step-by-step solving process

Example 1:

Step 1: Identify what’s happening to the variable

→ 7 is being added

Step 2: Undo it using the inverse operation

→ Subtract 7 from both sides

Example 2:

Step 1: Identify the operation

→ x is being multiplied by 3

Step 2: Undo it using division

→ Divide both sides by 3

Combining steps

Example 3:

Step 1: Subtract 4 from both sides

Step 2: Divide both sides by 2

Try it together (Parent + Student)

Say each step out loud before doing it.

Parents: ask“What operation is being done to x?”“How do we undo it?”

Independent practice

Students solve one-step and two-step equations using inverse operations and check their answers.

Common mistakes to avoid

• ❌ Performing operations on only one side

• ❌ Using the wrong inverse operation

• ❌ Forgetting to simplify

If you can explain why each step keeps the equation balanced, you understand algebraic solving.