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Tidy, Then Solve

Part of the Fundamentals section of Coddy's Algebra journey. Lesson 24 of 61.

A longer equation is solved with the same steps, with some simplifying first. To solve $2\left(x+1\right)+3x = 17$ , distribute first, then collect the like terms, then undo.

$2x+2+3x = 17$

$5x+2 = 17$

$5x = 15$

$x = 3$

After the first two lines, the equation is an ordinary two-step equation.

Distribute over the brackets, collect the like terms, and then isolate the unknown. In a long equation, simplify one part at a time before you decide which inverse operation to use.

Challenge

Medium

Solve $2\left(x+3\right)+4x = 30$ for $x$ .

Try it yourself

2\left(x+3\right)+4x = 30

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 Division Inverse Operations Recap: Two Moves in a Row

5Tidying First

Like Terms Terms and Numbers Mixed The Distributive Property Distributing a SubtractionTidy, Then SolveRecap: Tidying First

8Decimals and Percent

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

11Formulas

Using a Formula Finding a Missing Value Solving for a Letter Temperature Recap: Formulas

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