

A worksheet on solving compound inequalities. Students are required to solve pairs of inequalities and find their common solutions, graph the common solutions on the number line and write the common solutions using interval notation. Detailed solutions are included.
Are your secondary algebra students struggling to solve compound inequalities, find common solutions, or use set notation? This comprehensive, zero-prep practice worksheet is the perfect resource to help your students master combining inequalities with total confidence!
This resource transitions smoothly from introductory linear inequalities to rigorous multi-step systems, making it an excellent tool for deep conceptual practice, revision lessons, or exam preparation.
What is Included?
- 5 Robust Compound Inequality Challenge Tasks: Each multi-part problem contains a pair of linear inequalities that students must solve and evaluate to find the shared solution set.
- Scaffolded Skill Progression: Questions range from simple integer inequalities to highly advanced problems involving expanding brackets, collecting like terms, and clearing fractional coefficients.
- Visual Graphing Practice: Includes dedicated exercises for graphing the final solution sets onto a number line.
- Interval and Set Notation Integration: Challenges students to express their final solutions using formal interval notation brackets.
- Special Cases Included: Tests deeper mathematical understanding with unique outcome scenarios, including intersecting sets and “no solution” cases.
- Fully Worked Solutions Manual: A complete, step-by-step visual answers guide showing every line of algebraic work and every single number line graph for effortless marking, peer assessment, or self-checking!
Perfect For:
- Independent Classroom Practice
- Rigorous Homework Assignments
- GCSE Revision and Exam Prep
- Cover Lessons / Supply Teaching (Zero Prep Needed!)
- Small Group Intervention or Extension Tasks
Curriculum Alignment:
- Key Stage 3 (KS3) Maths: Excellent extension and challenge for higher-ability students in Years 8 and 9.
- Key Stage 4 (KS4) / GCSE Maths: Perfect core practice for both Foundation and Higher tier students (Years 10 and 11) covering the Algebra strand.
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