A worksheet on solving equations with one, none or infinitely many solutions. There are 24 problems. Detailed solutions are included.

Are your students confused about what happens when variables cancel out? Take the stress out of planning lessons on special cases with this comprehensive, ready-to-print linear equations worksheet and full solutions pack!
This resource is specifically designed to help learners master the differences between equations with one solution, no solution, or infinitely many solutions. It guides students smoothly from basic linear expressions to complex multi-step equations featuring brackets, expanding expressions, and algebraic fractions. It is an ideal resource for classwork, independent practice, homework, cover plans, or an end-of-unit revision booklet!

What is Included in This Download?

• Scaffolded Practice Problems: Carefully organized boxes that provide ample workspace for students to show their algebraic workings.
• Full Step-by-Step Solutions: Complete, fully worked-out answer keys for every single problem to save you hours of marking time and allow for easy student self-checking.
• No-Prep Needed: A ready-to-print PDF file that requires zero assembly time!

Key Skills & Topics Covered

• Recognizing Special Cases: Identifying the exact structural differences between standard solutions (x = a), no solution (0 = a), and infinitely many solutions (0 = 0).
• Collecting Like Terms: Simplifying multi-term expressions on both sides of the equal sign before solving.
• Distributive Law (Brackets): Multiplying across brackets safely to expand equations.
• Clearing Denominators (Fractions): Handling rational coefficients and multi-step fractional equations with confidence.

Target Audience & Year Groups:

• Key Stage 3 (KS3): Year 8 and Year 9 core curriculum practice and algebraic mastery.
• Key Stage 4 (KS4 GCSE): Perfect for GCSE Foundation tier practice or as a vital revision tool for Higher tier students tackling special cases.
• Differentiated Learning: Use individual sections for targeted intervention or print the whole document as a comprehensive homework pack.