Equations Worksheet — KS3 — Beginner
Equations worksheet for Key Stage 3 / Year 7-9 (Ages 11-14). Beginner level maths practice, aligned to the UK National Curriculum. Print-ready with answer key included.
Exploring Equations: A Beginner's Guide
Key Stage 3 / Year 7-9 (Ages 11-14) - Beginner Level
Instructions: This worksheet will guide you through the basics of solving equations. You will practice solving linear equations, understanding variables, and applying these skills to real-world problems. Follow the instructions for each activity and show your work clearly.
Solving Simple Equations
Solve each equation for x. Show all your working clearly in the space provided. Remember to check your solutions by substituting them back into the original equation.
1. x + 3 = 7
2. 2x - 4 = 10
3. 3x + 5 = 20
4. 4x - 8 = 12
5. 5x + 6 = 31
Understanding Variables
Identify the variable in each equation and explain in a sentence what it represents. Write your explanation in the box provided.
1. 2y + 5 = 15
2. 3z - 9 = 0
3. a/4 = 3
Applying Equations to Real-World Problems
Read each problem carefully and set up an equation to solve it. Write your equation and solution in the space provided.
1. Sarah has £15. She spends £3 on a book and wants to buy a pen that costs £x. How much does the pen cost if she has £5 left?
2. A car travels 60 miles in 2 hours. Write an equation to find the speed of the car in miles per hour.
Equation Word Problems
Translate each word problem into an equation and solve for the unknown variable. Write your answers clearly.
1. A number increased by 7 is 15. What is the number?
2. Three times a number decreased by 2 is 10. What is the number?
Equation Balancing
Balance each equation by performing the same operation on both sides. Write the balanced equation and solution.
1. x + 5 = 12
2. 2x - 3 = 7
3. 4x + 1 = 17
Exploring Algebraic Expressions
Simplify each algebraic expression by combining like terms. Write your simplified expression in the box provided.
1. 3x + 2x
2. 4y - y
3. 5a + 2a - a
Equation Creation
Create an equation based on the given scenario. Write the equation and solve for the unknown variable.
1. If the sum of a number and 9 is 20, what is the number?
2. A rectangle has a length of 10 cm and a width of w cm. If the perimeter is 30 cm, find w.
Data Analysis with Equations
Analyse the data in the table and use it to answer the questions below. Write your answers in the space provided.
| Item | Cost (£) | Quantity |
| Pen | 2 | 5 |
| Notebook | 3 | 4 |
| Eraser | 1 | 6 |
1. Write an equation to calculate the total cost of buying 5 pens.
2. How much would it cost to buy 3 notebooks?
Activity 1: x = 4 ; x = 7 ; x = 5 ; x = 5 ; x = 5
Activity 2: y = 5 ; z = 3 ; a = 12
Activity 3: x = 7 ; speed = 30
Activity 4: number = 8 ; number = 4
Activity 5: x = 7 ; x = 5 ; x = 4
Activity 6: 5x ; 3y ; 6a
Activity 7: number = 11 ; w = 5
Activity 8: Total cost = £10 ; Cost = £9
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