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Variable Substitution Practice

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Variable Substitution Practice

Variable Substitution Practice

Algebraic expressions with variables

🔢 Part 1: Basic Variable Substitution

1. If x = 4, find the value of x + 7
2. If y = 6, find the value of 3y - 2
3. If a = 5, find the value of 2a + 8
4. If m = 3, find the value of m² + 1
5. If n = 7, find the value of 15 - n

🚴 Part 2: Real-World Variable Problems

6. If x is the number of wheels on a tricycle, what is 2x + 5?

Step 1: How many wheels does a tricycle have? x = _____

Step 2: Substitute into 2x + 5 = 2(____) + 5

7. If h represents the number of hours you sleep (8 hours), what is 24 - h?

This tells you how many hours you are awake!

8. If p is the price of one pie ($4), what is 3p + $2 delivery?

🔄 Part 3: How Variables Affect Results

9. Complete the table for the expression 2x + 3:
x value 2x + 3 Result
1 2(1) + 3 _____
3 2(3) + 3 _____
5 2(5) + 3 _____
What pattern do you notice as x increases?

📐 Part 4: Simple Formulas (Extension)

10. Area of a rectangle = length × width. If l = 8 metres and w = 5 metres, find the area.

Formula: Area = l × w

11. Perimeter of a rectangle = 2l + 2w. Using the same values above, find the perimeter.
12. Distance = speed × time. If a car travels at 60 km/h for 2.5 hours, how far does it travel?

Let s = speed and t = time

Distance = s × t = _____ × _____ = _____ kilometres

🤔 Part 5: Understanding Variables

13. Circle the best definition of a variable:

A number that never changes

A letter that represents an unknown number

Only the letter x

A mathematical operation

14. If you change the value of a variable in an expression, what happens to the result?

The result stays exactly the same

The result usually changes

The expression becomes invalid

Nothing happens

15. Explain in your own words what it means to "substitute" a value for a variable:

🧩 Part 6: Variable Challenge

16. Match each expression with its value when x = 4:
1. x + 6
2. 3x
3. x² - 1
4. 20 ÷ x
A. 12
B. 5
C. 15
D. 10
17. Create your own variable problem using the variable t for temperature in °C:

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