Linear Equations Worksheet — KS3 — Intermediate

Linear Equations worksheet for Key Stage 3 / Year 7-9 (Ages 11-14). Intermediate level maths practice, aligned to the UK National Curriculum. Print-ready with answer key included.

Maths•Key Stage 3 / Year 7-9 (Ages 11-14)•Linear Equationsintermediate

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Exploring Linear Equations

Key Stage 3 / Ages 11-14 / Intermediate Level

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Instructions: This worksheet will guide you through solving and understanding linear equations. You will practice solving equations, interpreting data, and applying your knowledge to real-world problems.

Solving Linear Equations

Solve each equation for x. Show all your working clearly in the space provided.

1. 2x + 5 = 13

2. 3x - 7 = 11

3. 4x + 8 = 20

4. 5x - 10 = 15

5. 6x + 3 = 27

6. 7x - 14 = 21

7. 8x + 12 = 44

8. 9x - 18 = 36

Graphing Linear Equations

Plot the following linear equations on a graph. Use the grid provided to draw the lines.

1. y = 2x + 3

2. y = -x + 5

3. y = 3x - 2

4. y = -2x + 4

Interpreting Data from a Table

Analyse the data in the table below and answer the questions that follow.

Month	Temperature (°C)	Rainfall (mm)
January	5	78
February	7	60
March	10	55
April	12	42

1. Which month had the highest temperature?

2. Calculate the total rainfall for the four months.

3. What is the average temperature over the four months?

Word Problems Involving Linear Equations

Read each problem carefully and solve for the unknown variable. Show all your working.

1. A train travels at a constant speed. If it covers 150 miles in 3 hours, what is the speed of the train?

2. Sarah has £50. She spends £12 on a book and £15 on a gift. How much money does she have left?

3. A rectangle has a perimeter of 30 cm. If the length is twice the width, find the dimensions of the rectangle.

Identifying Solutions to Linear Equations

Determine if the given values are solutions to the equations. Write 'Yes' or 'No' in the box.

1. Is x = 3 a solution for 2x + 4 = 10?

2. Is x = -1 a solution for 3x - 5 = -8?

3. Is x = 5 a solution for x/2 + 3 = 5.5?

Creating Linear Equations from Word Problems

For each scenario, write a linear equation that represents the situation described.

1. A taxi charges a base fare of £3 plus £2 per mile. Write an equation for the total cost C for a trip of m miles.

2. A gym membership costs £20 per month plus an initial joining fee of £15. Write an equation for the total cost T after m months.

Solving Inequalities

Solve each inequality for x and represent the solution on a number line.

1. 3x + 4 > 10

2. 5x - 7 ≤ 18

3. -2x + 6 < 12

Real-World Application of Linear Equations

Read the scenario and use a linear equation to solve the problem. Explain your reasoning.

A company sells handmade candles. Each candle costs £5 to make and sells for £12. If the company wants to make a profit of £140, how many candles must it sell?

Answer Key

Activity 1: x = 4 ; x = 6 ; x = 3 ; x = 5 ; x = 4 ; x = 5 ; x = 4 ; x = 6

Activity 2: Graphs of the equations

Activity 3: April ; 235 mm ; 8.5°C

Activity 4: 50 mph ; £23 ; Length = 10 cm, Width = 5 cm

Activity 5: Yes ; Yes ; No

Activity 6: C = 3 + 2m ; T = 15 + 20m

Activity 7: x > 2 ; x ≤ 5 ; x > -3

Activity 8: 20 candles