📐 Part A: Solve the Equations

Instructions: Solve each equation by finding the value of the variable. Show your working and check your answer by substitution.

1. t + 5 = 13

2. 3p = 18

3. 4x + 2 = 14

4. 2y - 3 = 7

5. 6m = 42

6. 3n + 7 = 22

🔧 Part B: Simplify the Expressions

Instructions: Simplify each expression by expanding brackets and collecting like terms.

1. 3(a + 4) + 2

2. 2(m + 5) - 3m

3. 5 + (2x - 1)

4. 4(b - 2) + 3b

5. 2(3k + 1) - 4

🔍 Part C: Patterns and Rules

Instructions: Identify the pattern and write algebraic rules to describe the relationships.

1. Find the next 2 terms in this pattern: 2, 5, 8, 11, _____, _____

2. Write an algebraic rule for the pattern: 3, 6, 9, 12, 15, ...

Rule: ________________

3. Using your rule from question 2, find the 8th term.

4. Complete this pattern table and write the rule:

Position (n): 1, 2, 3, 4, 5

Value: 4, 7, 10, _____, _____

Algebraic rule: ________________

5. A tukutuku pattern follows the rule: Number of triangles = 5n + 2, where n is the row number. How many triangles are in row 6?

🧠 Part D: Word Problems

Instructions: Form an equation from each word problem, then solve it.

1. Sarah has some stickers. After giving away 8 stickers, she has 15 left. How many stickers did she start with?

Equation: ________________

2. A rectangle has a length that is 3 times its width. If the width is w centimetres and the perimeter is 32 centimetres, find the width.

Equation: ________________

3. The cost of hiring a bike is $15 plus $8 per hour. If the total cost was $47, how many hours was the bike hired for?

Equation: ________________

✅ Part E: Check Your Understanding

1. Which of these is the correct first step to solve 3x + 7 = 19?

Divide both sides by 3

Subtract 7 from both sides

Add 7 to both sides

Multiply both sides by 3

2. Select all the expressions that are equivalent to 2(x + 3):

2x + 6

x + 6

2x + 3

(x + 3) + (x + 3)

3. Explain in your own words what it means to "collect like terms":

4. True or False: The solution to an equation should always be checked by substitution.

True

False

5. Match each term with its definition:

1. Variable

2. Expression

3. Equation

4. Like terms

A. Mathematical statement with an equals sign

B. Terms with the same variable part

C. A letter representing an unknown number

D. Mathematical phrase without an equals sign

Linear Equations Practice

Linear Equations Practice

📐 Part A: Solve the Equations

🔧 Part B: Simplify the Expressions

🔍 Part C: Patterns and Rules

🧠 Part D: Word Problems

✅ Part E: Check Your Understanding

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