Equations with Variables on Both Sides Worksheet & Answer Key | 8th Grade

A worksheet on solving linear equations with variables on both sides. There are 24 problems and detailed solutions are included.

Looking for a clean, no-prep practice worksheet pack to help your pupils master solving equations with unknowns on both sides?

This comprehensive 24-question practice resource is specifically designed to build ultimate mathematical fluency. It features a beautifully structured, scaffolded progression of skills—starting with simple variable shifts and smoothly transitioning into equations with negative coefficients, zero solutions, and tricky sign rules on both sides of the equal sign.

Perfect for Key Stage 3 (KS3) core instruction, advanced Key Stage 2 (KS2) extension, or as a critical GCSE foundation and higher maths revision packet at the start of the term!

What’s Included:

• Pages 1–3 (24 Scaffolded Questions): A crisp, beautifully organized layout featuring large, clear question boxes that give pupils plenty of space to show their inverse operations and balancing work.
  Questions 1–8: Foundational balancing where unknowns can be grouped on one side quickly with positive and negative integer results.
  Questions 9–16: Progressively challenging equations introducing negative coefficients, moving constants, and fractional steps.
  Questions 17–24: Advanced combinations featuring balanced negatives, term grouping, and special solutions to test ultimate mastery.
• Full Step-by-Step Answer Key: Pages 4–6 contain a complete, beautifully written solutions guide showing every single algebraic step (inverse operations, moving variables, isolating constants, and integer division rules) for all 24 questions. This makes marking incredibly fast or allows for flawless pupil self-checking!

How to Use This in Your Classroom:

• Independent Classwork or Multi-Lesson Homework / Prep Assignment
• End-of-Unit Revision, Exam Prep, or Quiz Review
• Maths Mastery Workshops, Choice Boards, or Rotation Stations
• Emergency Cover Plans (the detailed answer key handles the teaching for you!)
• Small Group Intervention and Maths Remediation

Educational Standards & Curriculum Alignment:
UK National Curriculum (Key Stage 3 & 4 Mathematics):

• Algebra: Model situations or procedures by translating them into algebraic expressions or formulae and by using linear equations.
• Solve linear equations in one variable algebraically (including those with the unknown on both sides, with brackets, or containing fractions).