Introduction to Algebra – Variables, Terms, and Problem-Solving

Basic Algebra in Full | Lesson 1

🧠 What You’ll Learn

In this lesson, you’ll begin the language of algebra.

You’ll learn how to:

  • Translate simple statements into algebra
  • Represent numbers using letters
  • Understand variables, coefficients, and constants
  • Understand and identify like and unlike terms
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Watch Try Exercises Solutions ✅

🧩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.

🎯 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.

  1. Identify the variable in the expression $5x + 3$
  2. State the coefficient of $y$ in $7y – 4$
  3. Identify the constant in $2a + 9$
  4. How many terms are in the expression $3x + 5 – 2$?
  5. Write an algebraic expression for: “a number increased by $6$”
Show Answers
  1. $x$
  2. $7$
  3. $9$
  4. $3$
  5. $x + 6$

  1. Identify all the terms in the expression $4x + 3 – 2x + 7$
  2. Which of the following are like terms: $3x, 5y, 7x, 2$?
  3. Write an algebraic expression for: “twice a number decreased by $4$”
  4. Write an algebraic expression for: “a number increased by $3$, then multiplied by $2$”
  5. Mary’s age is $m$. Write an expression for John’s age if John is twice Mary’s age
Show Answers
  1. $4x, 3, -2x, 7$
  2. $3x$ and $7x$
  3. $2x – 4$
  4. $2(x + 3)$
  5. $2m$

  1. Identify all like terms in $2x + 5 + 3x – 4 + 7y$
  2. Write an algebraic expression for: “three more than twice a number”
  3. Paul’s age is $p$ and Mary’s age is $m$. Write an expression if Paul is $3$ years older than Mary
  4. Write an expression for: “the difference between twice a number and $5$”
  5. A number is increased by $4$ and the result is multiplied by $3$. Write the expression
Show Answers
  1. $2x$ and $3x$; $5$ and $-4$
  2. $2x + 3$
  3. $m + 3$
  4. $2x – 5$
  5. $3(x + 4)$

  1. Let Mary’s age be $m$. Write an expression for John’s age if John is three times the difference between Mary’s age and $2$
  2. Write an algebraic expression for: “twice the sum of a number and $5$, minus $3$”
  3. A service charges a $5$ dollar sign-up fee and $8$ dollars per month. Write an expression for the total cost after $n$ months
  4. Let $x$ be a number. Write an expression for: “four times the difference between $x$ and $3$”
  5. A number is doubled, then $6$ is added, and the result is multiplied by $2$. Write the expression
Show Answers
  1. $3(m – 2)$
  2. $2(x + 5) – 3$
  3. $5 + 8n$
  4. $4(x – 3)$
  5. $2(2x + 6)$

🔁 Continue Learning

⏮️ Back to Basic Algebra in Full
⏭️ Next Lesson → Lesson 2: Collecting Like Terms

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