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Algebraic Substitution and Simplification

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Algebraic Substitution and Simplification

Algebraic Substitution and Simplification

Algebraic expressions illustration

📝 Part 1: Basic Substitution

1. Substitute x = 3 into the following expressions and calculate the result:

a) 2x + 5 = ___________

b) 4x - 7 = ___________

c) 3x + 8 = ___________

2. Substitute y = 5 into these expressions:

a) 6y - 10 = ___________

b) 2y + 15 = ___________

🔢 Part 2: Multiple Choice - Order of Operations

3. When x = 4, what is the value of 3(x + 2)?

14

18

20

24

4. If a = 6, what is 2(a - 3) + 4?

8

10

12

16

🧮 Part 3: Simplifying Expressions

5. Simplify the following expressions by combining like terms:

a) 3x + 5x = ___________

b) 7y - 2y + 4 = ___________

c) 4a + 3b - 2a + b = ___________

6. Expand and simplify these expressions:

a) 2(x + 4) = ___________

b) 3(2y - 5) = ___________

c) 4(3m + 1) - 2m = ___________

⚡ Part 4: Challenge Problems

7. Substitute x = 2 and y = 3 into the following expressions:

a) 3x + 2y - 5 = ___________

b) 4(x + y) - 2x = ___________

8. Simplify completely, then substitute a = 4:

a) 5(a + 3) - 2(a - 1)

First simplify: ___________

Then substitute a = 4: ___________

🎯 Part 5: Error Analysis

9. A student made an error in the following problem. Identify the mistake and provide the correct answer:

Problem: Substitute x = 5 into 3(x - 2) + 4

Student's work: 3(5 - 2) + 4 = 3(3) + 4 = 9 + 4 = 13

Check all that apply:

The student made no error

The student incorrectly substituted the value

The student made an arithmetic error

The student forgot to follow order of operations

Correct answer: ___________

💭 Part 6: Reflection

10. Explain in your own words the steps you follow when substituting a value into an algebraic expression:
11. What is the most important thing to remember when simplifying expressions with brackets?

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