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Basic Algebra Foundations

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Basic Algebra Foundations worksheet preview
Basic Algebra Foundations

Basic Algebra Foundations

Algebra symbols and equations illustration

🔤 Part 1: Understanding Algebraic Terms

1. Match each algebraic term with its definition:
1. Variable
2. Coefficient
3. Constant
4. Expression
A. A number that doesn't change (like 7 in 3x + 7)
B. A letter that represents an unknown number (like x or y)
C. The number in front of a variable (like 3 in 3x)
D. A mathematical phrase with numbers and variables
2. In the expression 5x + 8, identify each part:

The coefficient is: ____________

The variable is: ____________

The constant is: ____________

➕ Part 2: Simplifying Expressions

3. Simplify these expressions by combining like terms:

a) 2x + 3x = ____________

b) 4y + 2y + 5 = ____________

c) 7a + 3 + 2a = ____________

4. Circle the expressions that are already simplified:

3x + 2

5y + 3y

8z + 4

2a + 6a + 1

🔢 Part 3: Substitution

5. Evaluate these expressions when x = 4:

a) 3x + 5

Answer: ____________

b) 2x + 7

Answer: ____________

6. If y = 6, what is the value of 4y + 3?

27

24

21

13

7. Real-world application: The cost of hiring a bike is $15 plus $8 per hour. Write this as an expression using h for hours:

Cost = ____________

If you hire the bike for 3 hours, what is the total cost?

Total cost: $____________

⚖️ Part 4: Solving Simple Equations

8. Solve these one-step equations:

a) x + 7 = 15

x = ____________

b) y - 3 = 12

y = ____________

c) z + 9 = 20

z = ____________

9. Check your answer: If x = 8, does x + 5 = 13?

Yes, because 8 + 5 = 13

No, because 8 + 5 = 14

No, because 8 + 5 = 12

10. Problem solving: Sarah has some stickers. After giving away 6 stickers, she has 14 left. How many stickers did she start with?

Write an equation: ____________

Sarah started with ____________ stickers.

🤔 Part 5: Reflection

11. Explain in your own words what it means to "solve an equation":
12. Give one example of where algebra might be useful in everyday life:

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