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Variables and Algebraic Expressions

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Variables and Algebraic Expressions

Algebraic expressions illustration

📚 Part 1: Understanding Variables and Expressions

1. What is a variable in algebra?

A number that never changes

A letter that represents an unknown number

The answer to a math problem

A type of calculator

2. In the expression 5x + 3, identify each part:

The coefficient is: ________

The variable is: ________

The constant is: ________

3. Which of these are algebraic expressions? (Check all that apply)

7 + 4

3n - 8

x = 12

2y + 5

✏️ Part 2: Real-World Scenarios

4. Maria has some stickers. She gives away 7 stickers to her friends. Write an algebraic expression for the number of stickers she has left.

Let s = the number of stickers Maria started with

Expression: ________________

5. A movie theater charges $12 per ticket. Write an expression for the total cost of tickets for a group.

Let t = the number of tickets purchased

Expression: ________________

6. Jake runs 3 miles every morning and some additional miles in the evening. Write an expression for his total daily miles.

Let e = evening miles

Expression: ________________

7. A pizza costs $15 plus $2 for each topping. Write an expression for the total cost of a pizza.

Let n = number of toppings

Expression: ________________

8. Sarah has twice as many books as her brother, plus 4 more books. Write an expression for the number of books Sarah has.

Let b = number of books her brother has

Expression: ________________

🎯 Part 3: Create Your Own

9. Write your own real-world scenario that can be represented by the expression 4x - 10.
10. Create an algebraic expression for this situation: "The school cafeteria serves the same number of students each day for 5 days, then serves 25 fewer students on Friday."

Let d = number of students served each regular day

Expression for total students served all week: ________________

📋 Answer Key

1. A letter that represents an unknown number

2. Coefficient: 5, Variable: x, Constant: 3

3. 3n - 8 and 2y + 5 (algebraic expressions contain variables)

4. s - 7

5. 12t

6. 3 + e

7. 15 + 2n

8. 2b + 4

9. Sample answer: "A gym membership costs $4 per month, but there's a $10 registration fee that gets refunded, so the expression represents the net cost after x months."

10. 5d - 25 or 4d + (d - 25)

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