Lesson 2.2

One-Step Equations (Multiply & Divide)

If a variable is multiplied by a number, divide it out. If it's divided, multiply it back. In algebra, every operation has an undo button.

Introduction

In Lesson 2.1, we used subtraction to undo addition. Now we tackle multiplication and division. The goal is the same: isolate the variable using inverse operations.

Past Knowledge

You can solve equations like using inverse operations.

Today's Goal

Solve one-step equations involving multiplication and division.

Future Success

Most complex equations end with a division step (e.g., ).

Key Concepts

1. Inverse Operations

To Undo Multiplication...

Divide by the same number.

To Undo Division...

Multiply by the same number.

2. The Golden Rule of Equality

Whatever you multiply or divide on one side, you must do to the other.

3. Checking Your Answer

Always plug your solution back into the original equation. If , does ? Yes.

Worked Examples

Example 1: Undoing Multiplication

Basic

Solve .

1

Divide Both Sides

The variable is multiplied by 4, so we divide by 4.

2

Simplify

Example 2: Undoing Division

Intermediate

Solve .

1

Multiply Both Sides

The variable is divided by -3, so multiply by -3.

2

Simplify

Example 3: Negative Coefficients

Advanced

Solve .

1

Divide by Negative

Divide by , not .

2

Simplify

Common Pitfalls

Forgetting the Sign

In , students often divide by 4 instead of -4, getting wrong. You must divide by the exact coefficient.

Subtracting Instead of Dividing

For , some try to subtract 3. But means , so you must divide to undo it.

Real-Life Applications

Unit conversion relies on multiplication and division equations. If you know that , finding the weight of a lb suitcase means solving . These equations are everywhere in science and engineering.

Practice Quiz

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