Basic Algebra in Full

This series is being released progressively. Lessons and exercises will appear here as they are completed.

Overview

This series introduces the language of algebra: variables, expressions, equations, and structured problem-solving. It builds the foundation for all further algebraic and advanced mathematical reasoning. Emphasis is placed on clarity, simplification techniques, and understanding how algebra represents real relationships.

Recommended Prior Study

Basic arithmetic only

Lesson Index

Lesson 1 – Introduction to Algebra
Lesson 2 – Collecting Like Terms
Lesson 3 – Addition & Subtraction
Lesson 4 – Multiplication & Division
Lesson 5 – Powers, Indices, Exponents & Roots
Lesson 6 – Removing Brackets (Coming Soon)
Lesson 7 – Algebraic Fractions (Coming Soon)
Lesson 8 – Order of Operations (Coming Soon)
Lesson 9 – Linear Equations (Coming Soon)
Lesson 10 – Word Problems (Coming Soon)

▶ Watch the full Basic Algebra in Full series on YouTube

Lesson 1: Introduction to Algebra

Variables, Terms, and Problem-solving

▶ Watch this Lesson on YouTube

▶ Watch the solution to the Try Exercise on YouTube

🎯 Suggested entry level (based on typical school curricula)

🇳🇬 Nigeria: JSS1 and above
🇬🇧 UK: Year 7 and above
🇺🇸 USA: Grade 6 and above
🇨🇦 Canada: Grade 6 and above
🇮🇳 India: Class 6 and above

Exercises

1. For each expression, identify and list all the Terms, Variables, Coefficients, and Constants:

7x + 4
−5a − 9
2a + b − 5 + 3c − d

2. A phone plan has no fixed fee but charges $0.05 per minute. Tom has talked for m minutes this month and his bill is $12.50. Write the equation and explain why this is simpler than the ones with a fixed fee.

3. Sarah buys a phone plan with a fixed monthly fee of $25 plus $0.10 per text message sent. Let t be the number of texts sent in a month. Write an expression for her total bill.

4. Emma is saving for a new bike that costs $120. She already has $45 saved and saves $15 each week. Let w be the number of weeks from now. Write an equation to show when she will have enough money (total savings = cost).

5. A farmer sells apples at $2 per kilogram plus a $6 box fee. If Mia buys k kilograms and pays $22 in total, write the equation to find k.