Numbers and x's Everywhere

Part of the Fundamentals section of Coddy's Math journey. Lesson 31 of 64.

7x - 4 = 3x + 8: the full pattern. Subtract 3x from both sides, add 4 to both sides, divide by 4.

4x - 4 = 8

4x = 12

x = 3

Check: 7 × 3 - 4 = 17 and 3 × 3 + 8 = 17.

Three moves, and the order of the first two does not matter: numbers first and x's second also works. What matters is the shape you are aiming for, x-terms on one side, numbers on the other, because from that shape one division finishes it.

Challenge

Solve the equation 8x - 3 = 5x + 12 for x.

Try it yourself

8x - 3 = 5x + 12

Solve for x

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Fundamentals

1What an Equation Is

The Equation Finding the Unknown The Same to Both Sides Solved Means Alone 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

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'sNumbers and x's EverywhereParentheses 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