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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: Warm-Up Review - One-Step Equations

1. Solve these one-step equations:

a) x + 7 = 15

b) 4y = 20

c) z - 9 = 12

2. What inverse operation would you use to solve each equation? Circle the correct answer:

For the equation x + 5 = 12:

Add 5 to both sides

Subtract 5 from both sides

Multiply both sides by 5

⚖️ Part 2: Introduction to Two-Step Equations

3. Complete the missing steps to solve this two-step equation:

Solve: 2x + 3 = 11

Step 1: Subtract _____ from both sides

2x = _____

Step 2: Divide both sides by _____

x = _____

4. Check your answer by substituting back into the original equation:

2(____) + 3 = _____ ✓

5. Circle the correct order of operations for solving two-step equations:

Undo multiplication/division first, then addition/subtraction

Undo addition/subtraction first, then multiplication/division

It doesn't matter which order you use

📝 Part 3: Guided Practice - Solving Two-Step Equations

6. Solve each two-step equation. Show all your working steps clearly:

a) 3x - 2 = 13

b) y/4 + 5 = 9

c) 2t + 7 = 19

d) 5m - 8 = 17

7. Check one of your solutions above by substituting back into the original equation:

🌟 Part 4: Real-Life Applications

8. Write and solve equations for these real-life situations:

a) Sarah buys 3 identical books and pays a $5 delivery fee. Her total cost is $32. How much does each book cost?

Equation: ________________

Each book costs: $______

b) The temperature dropped by 8°C overnight, then doubled during the day to reach 16°C. What was the temperature at the start of the day?

Equation: ________________

Starting temperature: ______°C

9. Create your own real-life word problem that requires a two-step equation to solve:

Your equation: ________________

🧩 Part 5: Challenge Problems

10. Solve these more challenging two-step equations:

a) 0.5x + 3 = 7

b) 2y/3 - 4 = 8

11. Fill in the blanks to complete this explanation:

To solve a two-step equation, I first undo the _____________ or _____________ operation, then I undo the _____________ or _____________ operation. This process is called using _____________ operations to _____________ the variable.

🎯 Part 6: Reflection

12. Explain in your own words the steps to solve a two-step equation:
13. What was the most challenging part of this lesson for you?

Remembering which operation to undo first

Keeping track of positive and negative numbers

Writing equations from word problems

Checking my answers by substitution

Understanding the vocabulary (isolate, inverse operations)

14. Rate your confidence level in solving two-step equations:

Very confident - I can solve them easily

Somewhat confident - I need a bit more practice

Not very confident - I need lots more help

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