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Inverse Operations

Part of the Fundamentals section of Coddy's Algebra journey. Lesson 7 of 61.

Inverse operations are operations that undo each other. There are two pairs.

Adding and subtracting: $x+7-7 = x$ .
Multiplying and dividing: $\frac{3x}{3} = x$ .

To solve, look at what was done to $x$ . Then do the inverse to both sides.

Use the number that is with $x$ . In $3x = 12$ , $x$ is multiplied by 3. So divide both sides by 3, not by 12. You get $x = 4$ .

Challenge

This time there are no suggestions. Write the next line yourself, until $x$ is alone.

Try it yourself

8x = 136

Get $x$ alone

All lessons in Fundamentals

1What an Equation Is

The Equation The Same to Both Sides Undoing Subtraction Recap: First Equations

4Two-Step Equations

Two Layers to Undo Subtract, Then Divide Add, Then Divide A Division Inside Negatives in Two Steps Recap: Two-Step Equations

7Fractions in Equations

A Fraction Coefficient Clearing One Denominator Two Denominators A Fraction Around a Sum Cross-Multiplying Recap: Fractions

10From Words to Equations

Phrases into Expressions Sentences into Equations Consecutive Numbers Age and Money A Perimeter Problem Recap: Words

2One-Step Equations

Undoing Multiplication Undoing DivisionInverse OperationsRecap: Two Moves in a Row

5Tidying First

Like Terms Terms and Numbers Mixed The Distributive Property Distributing a Subtraction Tidy, Then Solve Recap: Tidying First

8Decimals and Percent

Decimal Coefficients Two-Step with Decimals Adding a Percent Percent Equations Recap: Decimals

11Formulas

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3Negative Numbers

Below Zero A Negative Answer Negative Coefficients The Opposite of x Recap: Negatives

6Variables on Both Sides

x on Both Sides Gathering the x's Numbers and x's Everywhere Parentheses on One Side When x Is Negative Recap: Both Sides

9Special Cases

No Solution Always True Checking a Solution Recap: Special Cases

12Final Challenges

Parentheses on Both Sides Fractions and x's Decimals on Both Sides The Story Problem