Algebra Worksheet — KS3 — Beginner
Algebra 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.
Introduction to Algebra: Solving Equations
Key Stage 3 / Beginner Level
Instructions: This worksheet will introduce you to basic algebraic equations. Follow the instructions for each activity to solve the problems and improve your algebra skills.
Solving Simple Equations
Solve each equation for x. Show all your working clearly in the space provided.
1. x + 5 = 12
2. 2x - 3 = 11
3. 3x + 4 = 19
4. 4x - 5 = 15
5. 5x + 6 = 31
Equations with Fractions
Solve the following equations that include fractions. Express your answers in simplest form.
1. (1/2)x + 3 = 7
2. x/4 - 2 = 3
3. (3/5)x + 4 = 10
4. x/3 + 5 = 9
Word Problems
Translate each word problem into an equation and solve for x. Write your equation and solution in the space provided.
1. A number increased by 7 is 15. Find the number.
2. Three times a number decreased by 4 is 11. What is the number?
3. Five less than twice a number is 13. Determine the number.
Creating Equations
Create an equation based on the given scenarios and solve for x.
1. The sum of a number and 9 is equal to 20.
2. Double a number minus 7 equals 15.
Data Analysis with Equations
Analyse the data in the table and solve the equations based on the given conditions.
| Item | Cost (£) | Quantity | Total (£) |
| Apples | 2 | 5 | 10 |
| Oranges | 3 | 4 | 12 |
| Bananas | 1 | 6 | 6 |
1. If the cost of apples increases to £3 each, what will be the new total cost?
2. If 2 more oranges are purchased, what will be the new total cost for oranges?
Balancing Equations
Balance each equation by finding the value of x that makes both sides equal.
1. 3x + 5 = 2x + 10
2. 4x - 7 = 3x + 1
Inequalities
Solve the inequalities and represent the solution on a number line.
1. x + 3 < 8
2. 2x - 5 > 3
Substitution
Use substitution to solve the equations. Substitute the given value of x into the equation and find the result.
1. For x = 4, evaluate 2x + 3.
2. For x = -2, evaluate 3x - 5.
Activity 1: 7 ; 7 ; 5 ; 5 ; 5
Activity 2: 8 ; 20 ; 10 ; 12
Activity 3: 8 ; 5 ; 9
Activity 4: 11 ; 11
Activity 5: 15 ; 18
Activity 6: 5 ; 8
Activity 7: x < 5 ; x > 4
Activity 8: 11 ; -11
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