📝 Part 1: Forming Equations from Word Problems

1. A taxi fare is $5 plus $1.80 per kilometre. If the total fare is $18.20, write an equation to find the distance travelled.

Let d = distance in kilometres

Equation: ___________________

2. Sarah buys 3 packets of biscuits and pays an extra $2 for a drink. Her total cost is $14. Write an equation to find the cost of one packet of biscuits.

Let b = cost of one packet of biscuits

Equation: ___________________

3. A mobile phone plan costs $25 per month plus $0.50 for each text message. If the monthly bill is $37, write an equation to find the number of text messages sent.

Let t = number of text messages

Equation: ___________________

🔢 Part 2: Solving One-Step Equations

4. Solve: x + 7 = 15

Answer: x = _______

5. Solve: 4y = 28

Answer: y = _______

6. Solve: m - 9 = 12

Answer: m = _______

7. Solve: n ÷ 6 = 8

Answer: n = _______

⚡ Part 3: Solving Two-Step Equations

8. Solve: 3x + 5 = 20

Answer: x = _______

9. Solve: 2y - 7 = 11

Answer: y = _______

10. Solve: 4m + 3 = 19

Answer: m = _______

11. Solve: 5n - 8 = 17

Answer: n = _______

✅ Part 4: Checking Solutions

12. Check if x = 4 is the correct solution for 2x + 3 = 11

Substitute x = 4 into the equation:

Yes, x = 4 is correct

No, x = 4 is incorrect

13. Check if y = 6 is the correct solution for 3y - 5 = 13

Substitute y = 6 into the equation:

Yes, y = 6 is correct

No, y = 6 is incorrect

🧠 Part 5: Mathematical Vocabulary

14. Match each term with its correct definition:

1. Variable

2. Coefficient

3. Constant

4. Inverse operation

A. A number that doesn't change

B. The opposite operation used to solve equations

C. A letter that represents an unknown number

D. The number in front of a variable

15. Which of these are inverse operations? (Check all that apply)

Addition and subtraction

Multiplication and division

Addition and multiplication

Subtraction and division

🌟 Part 6: Problem Solving Challenge

16. A school fundraiser sells chocolate bars for $3 each. After paying $15 for supplies, they made a profit of $72. How many chocolate bars did they sell?

Step 1: Write an equation (let c = number of chocolate bars)

Step 2: Solve the equation

Step 3: Check your answer

Answer: They sold _______ chocolate bars.

17. Explain in your own words how to solve a two-step equation like 4x + 7 = 23