Simple Equations - Class 7 Mathematics (CBSE)
Based on the 2025-26 NCERT syllabus for Class 7 Mathematics. This chapter introduces the concept of algebraic equations -- setting them up from word problems and solving them systematically using balancing methods.
1. Why this chapter matters
Simple equations are the gateway to algebra. Every higher mathematics topic -- linear equations, quadratic equations, coordinate geometry -- builds on equation-solving skills. In CBSE exams, this chapter is worth 6-8 marks and connects directly to Class 8 Linear Equations in One Variable.
2. What is an equation?
An equation is a mathematical statement where two expressions are equal, connected by the equals sign (=).
An equation always has:
- A left-hand side (LHS)
- A right-hand side (RHS)
- An equals sign between them
- At least one variable (unknown quantity)
Example: 2x + 3 = 11
Equation vs expression
| Expression | Equation |
|---|---|
| 3x + 5 | 3x + 5 = 14 |
| No equals sign | Has an equals sign |
| Cannot be solved | Can be solved for the variable |
3. Setting up equations from word problems
Translation table
| Word/phrase | Mathematical symbol |
|---|---|
| is, are, equals | = |
| more than, sum, added to | + |
| less than, difference, subtracted from | - |
| times, product of, multiplied by | x |
| divided by, ratio | / |
| a number, some number | x (or any variable) |
Steps to set up an equation
- Read the problem carefully.
- Identify the unknown quantity and assign a variable.
- Translate the words into a mathematical equation.
- Solve the equation.
- Verify the solution.
4. Solving equations by balancing
The balance principle
Whatever operation you perform on one side of the equation, you must perform the same operation on the other side.
Solving steps
To isolate the variable:
- Add or subtract the same number on both sides.
- Multiply or divide both sides by the same non-zero number.
- Transpose terms (move terms from one side to the other, changing sign).
Transposition
Moving a term from one side to the other reverses its operation:
- Addition becomes subtraction and vice versa.
- Multiplication becomes division and vice versa.
5. Applications
Number problems
Example: A number increased by 12 is 25. Find the number. Equation: x + 12 = 25. Solution: x = 13.
Age problems
Example: Raj is 7 years older than Priya. Their total age is 33. Find their ages. Let Priya's age = x. Raj's age = x + 7. Equation: x + (x + 7) = 33. 2x + 7 = 33. 2x = 26. x = 13. Priya is 13, Raj is 20.
Geometry problems
Example: The perimeter of a rectangle is 40 cm. Its length is 5 cm more than its breadth. Find the dimensions. Let breadth = b cm. Length = b + 5 cm. Perimeter = 2(l + b) = 2(b + 5 + b) = 2(2b + 5) = 4b + 10 Equation: 4b + 10 = 40. 4b = 30. b = 7.5 cm. Length = 12.5 cm.
Money problems
Example: A total of Rs. 500 is divided between two friends such that one gets Rs. 80 more than the other. How much does each get? Let smaller share = x. Larger share = x + 80. Equation: x + (x + 80) = 500. 2x + 80 = 500. 2x = 420. x = 210. One gets Rs. 210, the other gets Rs. 290.
6. Worked examples
Example 1: Solve 3x - 7 = 14
Add 7 to both sides: 3x = 21. Divide by 3: x = 7. Verify: 3(7) - 7 = 21 - 7 = 14. Correct.
Example 2: Solve (y/4) + 3 = 5
Subtract 3 from both sides: y/4 = 2. Multiply by 4: y = 8. Verify: 8/4 + 3 = 2 + 3 = 5. Correct.
Example 3: Solve 2(x + 3) = 18
Divide both sides by 2: x + 3 = 9. Subtract 3: x = 6. Verify: 2(6 + 3) = 2 x 9 = 18. Correct.
Example 4: The sum of three consecutive numbers is 51. Find them.
Let numbers be x, x + 1, x + 2. Equation: x + (x + 1) + (x + 2) = 51. 3x + 3 = 51. 3x = 48. x = 16. Numbers: 16, 17, 18.
7. Common mistakes and how to fix them
| Mistake | Fix |
|---|---|
| Not transposing the sign correctly | When moving a term, reverse its operation |
| Forgetting to do same operation on both sides | Whatever you do to LHS, do to RHS too |
| Mistaking expression for equation | An equation must have an equals sign |
| Wrong variable assignment | Read carefully what the question asks for |
| Not verifying the answer | Substitute solution back into original equation |
8. CBSE exam focus
| Question type | Marks | Frequency |
|---|---|---|
| Solve simple equation | 2 marks | 1-2 questions |
| Set up equation from statement | 2 marks | 1 question |
| Word problem (age/number) | 3 marks | 1 question |
| Geometry application | 3 marks | Occasional |
| Equation with brackets | 3 marks | 1 question |
9. Self-test
- Solve: 5x - 3 = 22.
- Solve: (2y/3) + 1 = 7.
- Solve: 4(2x - 1) = 28.
- The sum of two numbers is 45. One number is 9 more than the other. Find the numbers.
- Rohan's father is 3 times as old as Rohan. The sum of their ages is 48. Find Rohan's age.
- The length of a rectangle is 4 cm more than its width. The perimeter is 48 cm. Find the length and width.
10. Answer key
- 5x = 25. x = 5.
- 2y/3 = 6. 2y = 18. y = 9.
- 2x - 1 = 7. 2x = 8. x = 4.
- Let numbers be x and x + 9. 2x + 9 = 45. 2x = 36. Numbers: 18 and 27.
- Let Rohan = x years. Father = 3x. 4x = 48. x = 12. Rohan is 12 years old.
- Let width = w. Length = w + 4. 2(w + w + 4) = 48. 4w + 8 = 48. 4w = 40. w = 10 cm, length = 14 cm.
11. Quick revision
- An equation states that two expressions are equal.
- To solve, isolate the variable using inverse operations.
- Whatever you do to one side, do to the other.
- Transposition changes the sign or operation.
- Always verify by substituting the answer back.
- Set up equations by carefully translating word statements.
