Algebraic Expressions and Simple Equations: Class 7 Study Guide
Algebra is the language of patterns. It lets us solve problems with unknown quantities.
An algebraic expression is made of variables, constants and operations, such as 3x + 5y − 2. The parts added or subtracted are terms. Like terms have the same variables raised to the same powers (3x and −5x are like terms; 3x and 3x² are not). The number in front of a variable is its coefficient.
An equation says two expressions are equal. Solving it means finding the value of the variable that makes it true. The key idea is balance: whatever you do to one side, do to the other.
Simplifying expressions
Add or subtract like terms: 4x + 3y − x + 2y = 3x + 5y. Use the distributive property to expand: 3(2x − 4) = 6x − 12. To find the value of an expression, substitute: if x = 2 and y = 3, then 3x + 5y = 6 + 15 = 21.
| Expression | Simplified |
|---|---|
| 2a + 5a | 7a |
| 6p − 2p + 3 | 4p + 3 |
| 4(x + 2) | 4x + 8 |
| 3m + 2n − m | 2m + 2n |
Solving equations
Use inverse operations. x + 9 = 14 → x = 5. 4x = 36 → x = 9. 3x − 5 = 16 → 3x = 21 → x = 7. 2(y + 3) = 14 → y + 3 = 7 → y = 4. Always check by substituting back.
Expand brackets, collect like terms.
Both sides.
Both sides.
Substitute in the original.
Word problems
Define the unknown, write the equation, solve and check. Example: 'The sum of a number and twice itself is 36.' x + 2x = 36, 3x = 36, x = 12. Example: Ria is 4 years older than Sam. The sum of their ages is 30. Sam's age s: s + (s + 4) = 30, 2s = 26, s = 13, so Ria is 17.
Common mistakes
Common mistakes: adding unlike terms (3x + 2y ≠ 5xy), forgetting to multiply every term inside brackets, changing only one side of the equation and mixing up 2x (twice x) and x² (x squared). Write each step on its own line.
Check your understanding: model answers
1. 3a + 3b. 2. x = 6. 3. 2n + 3 = 17, so n = 7.
✨ Key Takeaways
- Combine like terms only.
- Keep equations balanced.
- Use inverse operations.
- Check by substituting.
💬 Questions for Discussion & Reflection
- Simplify 5a + 3b − 2a.
- Solve 4x + 7 = 31.
- Twice a number plus 3 is 17. Find the number.