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Last updated

30 June 2026

pdf, 70.34 KB
pdf, 70.34 KB

A no prep worksheet on solving linear multi-step inequalities with fractions. Some of the inequalities have the variable on both sides and brackets. There are 16 problems and detailed solutions are included.

Master solving inequalities involving fractions with this ready-to-print practice worksheet!

Help your KS3 and KS4 (Year 8, Year 9, and GCSE Maths) students build confidence with multi-step algebraic inequalities. Algebraic fractions can often worry students, but this worksheet provides clear, structured practice to help them master the steps. The variety of problems challenges students to clear denominators, expand brackets, and successfully navigate the negative coefficient rule (flipping the inequality sign).

The best part? A complete step-by-step solution answer key is included, saving you valuable marking time!

What is Included?

  • 16 multi-step inequality problems that naturally progress in difficulty.
  • Fractions in every question to build true numerical and algebraic fluency.
  • Fully worked step-by-step solutions for every single question.
  • Clean layout with plenty of workspace for students to show their workings.

Ways to Use This Resource

  • Homework Assignment: Perfect for independent retrieval practice.
  • Cover Lessons: Ideal to leave for a cover teacher because the solutions are completely worked out.
  • Revision / Exam Prep: A thorough review of linear inequalities before end-of-term or GCSE exams.
  • Extension Tasks: Excellent challenge work for high-attaining pupils.

Curriculum Standards Covered

  • UK National Curriculum (KS3/KS4 Maths): Solve linear inequalities in one variable, including those with fractional coefficients, and represent the solution set algebraically.

Get this resource as part of a bundle and save up to 41%

A bundle is a package of resources grouped together to teach a particular topic, or a series of lessons, in one place.

Bundle

Solving & Graphing Inequalities Worksheets Bundle | Algebra 1 Homework Practice

Four worksheets on solving one-step, two-step and multi-step inequalities and on inequality representations. There is one worksheet on converting given inequalities to number lines and intervals, one worksheet on solving one-step and two-step inequalities and graphing their solution on the number line, one worksheet on solving linear multi-step inequalities with fractions and one worksheet on solving multi-step inequalities. Detailed solutions to all worksheets are included. **Are your students struggling to solve multi-step inequalities, flip signs with negative numbers, or master interval notation?** Take the stress out of your lesson planning with this comprehensive, print-and-go maths practice collection. This resource features a series of clean, structured practice worksheets designed to build confidence at every stage of your inequalities topic. It is the perfect addition to your Key Stage 4 (KS4) or GCSE maths lessons on solving linear inequalities, shading regions on number lines, domain, and range. **What's Included in This Resource?** * **Inequality Representations & Notation:** Guided table practice where students match inequality expressions, shade number lines, and write correct interval notation. * **One-Step and Two-Step Inequalities:** Essential foundations of solving and graphing, complete with plenty of workspace for students to layout their algebra. * **Multi-Step Inequalities:** Advanced practice that challenges students to expand brackets, collect like terms, and work with unknown variables on both sides. * **Inequalities with Fractions:** True rigorous extension practice that guides students through clearing denominators and solving complex rational inequalities. * **Step-by-Step Answer Keys:** Fully worked-out solutions are included for every single question to make marking a breeze or to allow for quick student self-assessment. **Why Teachers Choose This Resource** * **Zero Preparation Required:** Just print and copy. Perfect for daily homework, independent classwork, cover lessons, or structured exam revision. * **Scaffolded Skill Building:** Moves smoothly from basic number line matching to complex fractional equations to help you differentiate for all abilities in your classroom. * **High-Quality Layouts:** Clean, box-style grids give students plenty of physical space to write out their equations neatly and clearly. **Curriculum Standards Met** * **UK National Curriculum (Key Stage 4):** Solve linear inequalities in one variable and represent the solution set on a number line or using set notation. * **GCSE Maths Specifications (AQA, Edexcel, OCR):** Understand, use, and solve linear inequalities, including flipping inequality symbols when multiplying or dividing by a negative number. * **Mathematical Precision:** Encourages students to be precise when using open versus closed circles on number lines and parentheses versus square brackets in interval notation.

£3.50

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