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Algebra Basics Worksheet

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Algebra Basics Worksheet

Algebra symbols and equations

📚 Part 1: Key Definitions & Multiple Choice

Key Terms:

Variable: A letter that represents an unknown number (e.g., x, y, a)

Expression: A combination of numbers, variables and operations (e.g., 3x + 5)

Equation: A mathematical statement showing two expressions are equal (e.g., 2x + 1 = 7)

Term: A single number, variable, or number multiplied by variables (e.g., 5, x, 3y)

Formula: An equation that shows the relationship between variables (e.g., A = l × w)

1. Which of the following is a variable?

7

x

+

15

2. Which is an equation?

3x + 2

5y - 1 = 9

4a

x + y

3. Select all expressions below:

2x + 3

y = 5

4a - 7

3m + 1 = 10

4. How many terms are in the expression 5x + 3y - 2?

2

3

4

5

5. What is the coefficient of x in 7x + 2?

2

7

x

9

6. Which expression means “8 less than a number n”?

8 - n

n + 8

n - 8

8n

7. Which pair contains like terms?

3x and 5x

2a and 2b

7 and y

x and x²

8. Select all constants below:

12

4x

-3

y + 6

✏️ Part 2: Writing Expressions & Equations

9. Write an expression for "5 more than a number x":
10. Write an expression for "3 times a number y, minus 4":
11. Write an equation for "A number n plus 7 equals 15":
12. The cost of hiring a car is $50 plus $25 per day. Write a formula for the total cost C after d days:
13. Write an expression for "twice a number p plus 6":
14. Write an expression for "10 divided by a number q":
15. Write an equation for "4 times a number r equals 28":
16. Write an equation for "The difference between a number t and 9 is 13":
17. Write an expression for the perimeter of a rectangle with length l and width w:
18. Write an equation for "A number b divided by 5 equals 6":

🔢 Part 3: Simplifying Expressions

19. Simplify: 3x + 5x
20. Simplify: 9y - 4y
21. Simplify: 2a + 6 + 3a
22. Simplify: 8m - 3 + 2m + 7
23. Simplify: 5p + 2q + 3p
24. Simplify: 10z - 4z + 2

🧮 Part 4: Solving Simple Equations

25. Solve: x + 4 = 11
26. Solve: 2y = 14
27. Solve: 3x + 1 = 10
28. Solve: 5a - 3 = 17
29. Solve: n - 8 = 12
30. Solve: 4b + 6 = 26

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