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Sentences into Equations

Part of the Fundamentals section of Coddy's Algebra journey. Lesson 48 of 61.

A sentence with "is" or "equals" in it can be written as an equation. The word "is" becomes the equals sign. Take the sentence "5 more than twice a number is 17". Call the number $n$ and translate:

$2n+5 = 17$

Now you have a two-step equation. Subtract 5 from both sides, then divide by 2, and you get $n = 6$ . Check the answer against the sentence, not only against the equation. Twice 6 is 12, and 5 more than 12 is 17. The answer is right.

Every word problem follows the same steps. Name the unknown with a letter. Translate the sentence into an equation. Solve the equation. Then check the answer against the original words, including any units or conditions the problem gives.

Challenge

Medium

“4 less than three times a number is 20.” Write this sentence as an equation, using $n$ for the number. Do not solve it.

Start the lesson to read it in the interactive player and track your progress.

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 ExpressionsSentences into EquationsConsecutive 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