A worksheet on solving linear equations involving various cases such as: one-step and two-step linear equations, linear equations with brackets, linear equations with double brackets, linear equations with fractions and linear equations with the variable on both sides. Detailed solutions are included.

Master solving linear equations with this no-prep KS3/KS4 maths worksheet. Covers directed numbers, brackets, algebraic fractions & full worked solutions!

Looking for a rigorous, print-and-go resource to help your pupils master solving linear equations with positive and negative numbers?
This comprehensive maths worksheet is designed to build procedural fluency and algebraic reasoning across single-variable equations. Moving sequentially from fundamental balancing operations to equations containing brackets and complex algebraic fractions, this pack provides an exceptional match for Key Stage 3 (KS3) and Key Stage 4 (KS4) Higher or Foundation Tier GCSE preparation, or early secondary homework and revision modules.

What is Included in This Download?
• Section 1: Linear Foundations & Unknowns on Both Sides – 18 targeted equations establishing core isolation rules. Problems progress intentionally from basic integer operations to variables on both sides, collecting like terms, and handling negative coefficients (e.g., -3a = -12 or 6 - 5x = -6 - 2x).
• Section 2: Expanding Brackets & Parentheses – 10 multi-step equations requiring pupils to expand brackets accurately. This section specifically targets common pitfalls, such as distributing a negative sign across a binomial expression (e.g., -4(x - 1) = 20 or y - (2y + 4) = 10).
• Section 3: Fractional Equations & Algebraic Fractions – 10 advanced equations featuring fractional coefficients and multi-term numerators. Pupils practice finding common denominators and multiplying through to clear fractional denominators (e.g., (2x + 8)/2 - (x - 4)/5 = 4).
• Full Worked Solutions – A complete teacher memorandum matching every page, showing every single balancing move, fraction conversion, common denominator calculation, and sign change for effortless marking, peer assessment, or student self-checking.

Why Teachers Love This Resource:
• Zero Prep Required: Simply download, print, and distribute directly to your classes—perfect for main lessons, homework tasks, or emergency cover work.
• Differentiated Rigour: Problems naturally scale from fundamental directed number mechanics to challenging multi-step algebraic fraction extension questions.
• Versatile Use: Ideal for independent classwork, numeracy intervention groups, or standalone revision worksheets.

Curriculum & Exam Board Alignment:
• UK National Curriculum: Key Stage 3 (KS3) and Key Stage 4 (KS4) Mathematics – Algebraic proficiency, simplifying and manipulating algebraic expressions, and solving linear equations.
• Exam Boards: Highly relevant for Edexcel, AQA, and OCR GCSE Maths modules.