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Two-Step Linear Equations

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Two-Step Linear Equations worksheet preview
Two-Step Linear Equations

Two-Step Linear Equations

Algebraic equations illustration

🔢 Part 1: Understanding Two-Step Equations

1. Circle the equations that are two-step linear equations:

3x + 5 = 17

x + 8 = 12

2y - 7 = 11

4x = 20

6m + 3 = 21

2. For the equation 4x + 9 = 25, what are the two operations being performed on x?

First operation: _________________ Second operation: _________________

3. To solve 4x + 9 = 25, which operation should you undo first?

Subtract 9

Divide by 4

Add 9

Multiply by 4

📝 Part 2: Solving Two-Step Equations

4. Solve: 3x + 7 = 22

Answer: x = _______

5. Solve: 5y - 8 = 17

Answer: y = _______

6. Solve: 2m + 11 = 19

Answer: m = _______

7. Solve: 4n - 6 = 14

Answer: n = _______

✓ Part 3: Checking Solutions

8. Check if x = 4 is the correct solution for 3x + 5 = 17. Show your working:

Is x = 4 correct? Circle: YES / NO

9. Check if y = 6 is the correct solution for 2y - 3 = 9. Show your working:

Is y = 6 correct? Circle: YES / NO

10. Solve 6x - 4 = 20, then check your answer by substitution:

Solving:

Answer: x = _______

Checking:

🌟 Part 4: Real-World Applications

11. Sarah buys 3 identical books and pays a $5 delivery fee. Her total cost is $32. Write and solve an equation to find the cost of each book.

Equation: _________________________

Cost of each book: $______

12. A taxi charges $4 per kilometre plus a $7 booking fee. If the total fare is $31, how many kilometres was the journey?

Equation: _________________________

Distance travelled: ______ kilometres

13. Tom's age doubled plus 8 years equals 26 years. How old is Tom now?

Equation: _________________________

Tom's current age: ______ years

🎯 Part 5: Challenge Problems

14. Solve: 7x + 12 = 5x + 20

Answer: x = _______

15. Solve: 3(y + 4) = 21

Answer: y = _______

16. Fill in the missing number: 4x + _____ = 23, when x = 5
17. Reflection: Explain in your own words the steps you follow to solve a two-step linear equation.

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