Linear Inequalities Worksheet - KS3 Maths

Teach KS3 pupils to solve linear inequalities and represent solutions on number lines with worked examples, differentiated practice and full solutions.

This print-ready linear inequalities worksheet pack develops understanding step by step rather than relying on the unexplained instruction to “flip the sign”. Pupils connect inequality language, symbols and number-line representations before progressing from one-step inequalities to negative coefficients, brackets, variables on both sides and contextual problems.

The worked section explains why multiplying or dividing an inequality by a negative number reverses its direction. Pupils connect this rule to the order of numbers on a number line and practise choosing correct open or closed endpoints, shading in the correct direction and checking values from a solution set.

What is included

• 15-page A4 pupil workbook
• 41 carefully sequenced questions
• Five-question prerequisite and readiness check
• Five fully worked examples
• Five faded examples for guided practice
• 32 differentiated practice questions
• Inequality symbols, words and number-line representations
• One-step inequalities with positive and negative coefficients
• Two-step and multi-step linear inequalities
• Brackets and variables on both sides
• Four contextual inequality problems
• Four misconception-based error-analysis tasks
• Five-question exit check
• 13-page complete worked-solutions file
• KS3 teacher guide
• Five-page product preview

Designed for

• KS3 Maths, particularly Years 8–9
• Whole-class teaching
• Algebra intervention and catch-up
• Small-group work and tutoring
• Independent practice or homework
• GCSE Foundation revision where appropriate

Differentiation and progression

The practice is divided into genuinely different stages.

Level 1 focuses on inequality language, symbols and number-line representation. Level 2 develops one-step inequalities, including negative coefficients. Level 3 and the challenge section introduce variables on both sides, brackets, mixed representations and contextual constraints.

The teacher guide includes prerequisite knowledge, a suggested readiness threshold, common misconceptions, differentiation guidance, assessment notes and suggested 45-, 60- and 90-minute teaching routes.

Curriculum and prerequisites

This resource is designed to support KS3 algebra involving linear inequalities in one variable and representing solution sets on a number line. It can also support GCSE Foundation revision. Teachers should confirm alignment with their own scheme of learning.

Pupils should already be able to order directed numbers, use inverse operations, expand a single bracket, collect like terms and solve basic linear equations.