Linear Equations in One Variable – How to Find $x$

🧠 What You’ll Learn

In this lesson, you’ll learn how to solve linear equations in one variable by understanding the mathematical principles behind finding unknown values. Rather than memorising procedures, you’ll learn how algebraic operations, inverse operations, fractions, roots, and formula rearrangement all work together to isolate a variable and reveal its value.

You’ll learn how to:

• Understand why variables cannot be solved from expressions and require equations
• Distinguish clearly between algebraic expressions and algebraic equations
• Understand the ultimate goal of equation solving: isolating the variable
• Use inverse operations to undo addition, subtraction, multiplication, division, powers, and roots
• Solve simple linear equations in one variable step by step
• Collect like terms when variables appear on both sides of an equation
• Apply algebraic operations correctly to both sides of an equation
• Avoid common mistakes when working with entire sides of equations involving multiple operations
• Understand why brackets are sometimes required when applying operations to an entire expression
• Solve equations involving fractions using inverse operations
• Use cross multiplication correctly and understand when it is valid
• Solve equations involving square roots and other roots
• Recognise how roots and powers act as inverse operations
• Understand the core mathematical principle that underlies all equation solving
• Learn what it means to make a variable the subject of a formula
• Rearrange formulae using the same logical process used for solving equations
• Change the subject of a formula when variables are connected through addition, subtraction, multiplication, division, fractions, and brackets
• Solve equations involving bracket expansion and the distributive law
• Apply previous algebra skills such as collecting like terms, removing brackets, simplifying fractions, and order of operations
• Solve equations involving algebraic fractions and multiple denominators
• Work confidently with equations containing surds and square roots
• Simplify surds using factorisation and root extraction techniques
• Combine multiple algebraic techniques within longer multi-step problems
• Develop a systematic approach to solving increasingly complex algebraic equations
• Check and verify solutions by substitution
• See how all previous lessons in the series connect together to make equation solving possible

By the end of this lesson, you’ll be able to confidently solve linear equations in one variable, rearrange formulae, work with fractions and roots inside equations, and apply a structured problem-solving approach to a wide range of algebraic situations.

🧩Practice Exercises

These exercises help you build from foundation to advanced understanding.

You can:

• Start at your level
• Or work through all levels step by step

✍️ Attempt exercises before checking answers.

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🎯 Levels

Each level matches a stage of learning and shows
what you should be able to understand and solve at that point.

🟢 Foundation → You’re learning this topic for the first time
🟠 Developing → You understand the basics and are building on them
⚪ Confident → You’re ready for deeper, multi-step problems
⚫ Advanced → You want to challenge your understanding further

📘 Not sure where you fit? → View Level Guide

💡 Each set of exercises is designed to match what students at that stage are typically expected to handle.

Start with your level, then try the next one when you feel ready.

❓ Need Help?

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💬 Or leave a comment on the lesson video

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