The Same to Both Sides

Part of the Fundamentals section of Coddy's Algebra journey. Lesson 2 of 61.

$A level balance: x and 28 on the left pan, 75 on the right$

The balance is level. The left pan holds $x$ and 28. The right pan holds 75. Both sides weigh the same, so $x+28 = 75$ .

Take 28 off the left pan. Take 28 off the right pan too. The balance is still level, and only $x$ is left on the left.

$x+28-28 = 75-28$

$x = 47$

If you do the same to both sides, the equation stays true. You do not need to guess.

Challenge

Find $x$ without guessing. Pick what to do to both sides, and the board works out each side for you. Done means $x$ is alone on one side and a number is on the other.

Try it yourself

x+37 = 81

Get $x$ alone

All lessons in Fundamentals

1What an Equation Is

The EquationThe Same to Both SidesUndoing 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

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