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Algebra Basics Worksheet

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Algebra Basics Worksheet

Algebra symbols and equations

🔢 Part 1: Understanding Algebraic Expressions

Remember: In algebra, we use letters (like x, y, a, b) to represent unknown numbers or variables.

1. Which of the following are algebraic expressions?

3x + 5

12 + 8

2y - 7

15

2. If x = 4, what is the value of 3x + 2?

9

14

11

12

3. Simplify these expressions by collecting like terms:

a) 5x + 3x = __________

b) 7y - 2y + 4 = __________

c) 2a + 3b + 5a - b = __________

⚖️ Part 2: Solving Linear Equations

Remember: To solve equations, we need to get the variable by itself. Whatever we do to one side, we must do to the other side!

4. Solve for x: x + 7 = 15
5. Solve for y: 3y = 21
6. Solve for a: 2a - 5 = 11
7. Check your answer from question 6 by substituting back into the original equation:

📝 Part 3: Word Problems & Extension Activities

8. Sarah buys some notebooks for $3 each and pays a total of $18. Write an equation to find how many notebooks she bought, then solve it.

Equation: _______________

Answer: Sarah bought _______ notebooks.

9. The perimeter of a rectangle is 24 metres. If the width is 4 metres, find the length. (Hint: Perimeter = 2 × length + 2 × width)
10. Extension Challenge: Solve for x: 4(x - 3) = 2x + 6

Hint: First expand the brackets, then collect like terms.

11. Extension Challenge: Create your own word problem that leads to the equation 5x + 10 = 35, then solve it.

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