One-Step Linear Equations

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📚 Part 1: Writing Equations from Word Problems

Instructions: Read each scenario and write a one-step equation. Use the variable given in brackets.

1. The Year 7 class needs to buy decorations for their school dance. They spend $15 on streamers and $x on balloons. The total cost is $28. Write an equation to find the cost of balloons. (Use x)

Equation: _______________________

2. Sarah is buying notebooks for her group project. Each notebook costs $4 and she buys n notebooks. The total cost is $20. Write an equation to find how many notebooks she bought. (Use n)

Equation: _______________________

3. The school canteen sells meat pies for $m each. Tom buys 3 pies and pays $15 in total. Write an equation to find the cost of one pie. (Use m)

Equation: _______________________

4. A class is organising a fundraiser. They already have $45 and need to raise $t more to reach their goal of $82. Write an equation to find how much more they need. (Use t)

Equation: _______________________

⚖️ Part 2: Solving One-Step Equations

Instructions: Solve each equation using inverse operations. Show your working and check your answer by substitution.

5. Solve: x + 12 = 19

Solution: x = _______ Check: _______ + 12 = 19 ✓

6. Solve: 5y = 35

Solution: y = _______ Check: 5 × _______ = 35 ✓

7. Solve: w + 8 = 23

Solution: w = _______ Check: _______ + 8 = 23 ✓

8. Solve: 6z = 42

Solution: z = _______ Check: 6 × _______ = 42 ✓

🎯 Part 3: Real-World Problem Solving

Instructions: For each problem, write an equation, solve it, and explain what your answer means in the context.

9. The school's environmental club is buying native plants. Each plant costs $7 and they spend a total of $56. How many plants did they buy?

Equation: _______________________

Answer: The club bought _______ plants.

10. Year 7 students are collecting money for a charity. They have already collected $127 and need $200 in total. How much more money do they need to collect?

Equation: _______________________

Answer: They need to collect $_______ more.

11. Challenge: Create your own real-world scenario that can be solved using a one-step equation. Write the problem, equation, and solution.