Solving linear equations

Ages 13 to 17 Read alone · about 45 minutes

Read together

An equation says two expressions are equal. To solve 2x + 5 = 17, find the value of x that makes it true. Think of a balance: whatever you do to one side, you must do to the other.

Subtract 5 from both sides: 2x = 12. Divide both sides by 2: x = 6. Check: 2 × 6 + 5 = 17. It works.

The word algebra comes from al-jabr, “restoring”, in the title of a book by the mathematician al-Khwarizmi, about 1,200 years ago.

Do it

1. Solve these and check each: x + 7 = 15, 3x = 21, 4x − 3 = 13, 5x + 2 = 3x + 10.
2. Write a word problem for one of them: “I have saved some money. After adding 5 more I can buy a 17-peso item twice.” Solve it.
3. Use a bar model or a balance with objects to show the steps.
4. Check: substitute your answer back into the original equation.

Talk about it

• Why must you do the same to both sides?
• How can you check your answer?

For the grown-up

Understanding why the steps work, not just how, helps students succeed in later algebra. If your teen is stuck, ask them to explain the balance idea in their own words.

Mark as done

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Where this comes from

• Victor J. Katz, A History of Mathematics: An Introduction, 3rd ed. (Pearson, 2008), on al-Khwarizmi and the origins of algebra
• Common Core State Standards Initiative, Mathematics Standards, Expressions and Equations, grades 7 to 8 and Algebra

Written with AI assistance and checked against the sources listed. Please read it before sharing it with a child.