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Combining Like Terms

Overview

Apples with Apples.

What is it?

Simplifying expressions by adding or subtracting terms that have the exact same variable part.

History

The key step to solving multi-step equations.

Key Idea

Look at the 'Last Name' (variable). Only families can hang out together.

Practice This Topic

Concept Guide

Plain English: You can't add '3 chairs' and '2 tables' to get '5 chables'. They are different. In math, you can only combine x's with x's, and regular numbers with regular numbers.

Real-world example: Inventory lists. Combining counts from two different warehouses.

How to do it

  1. Circle all terms with the same variable (e.g., all x's). Include the sign in front!
  2. Box all plain numbers (constants).
  3. Add/Subtract the coefficients (numbers in front) of the circled group.
  4. Combine the boxed group.
  5. Write the final result.
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Common Pitfall

Combining x and x². They look similar, but x is a line and x² is a square. They cannot be added.

Word Problem
"You order 2 burgers and 1 fry. Your friend orders 1 burger and 2 fries. What is the table total?"
Reasoning: 2b + 1f + 1b + 2f. Combine b's: 3b. Combine f's: 3f. Total: 3b + 3f.

Practice Examples

Simplify
3x + 5 - 2x + 2 (3x-2x) + (5+2) 1x + 7
Group matching terms.