NCERT Solutions for Class 7th Maths Chapter 7 Finding the Unknown
Updated on 2026-09-19
About this chapter
A statement of equality between two algebraic expressions is called an equation . The part left of the '=' sign is the LHS , the part right of it is the RHS . Solving an equation means finding the value of the letter-number that makes LHS = RHS. Checking a solution means putting the value back in and seeing that both sides agree. A balanced weighing scale stays balanced when you remove the same weight from both pans. In exactly the same way, an equation stays true when the same operation is done on both sides — add, subtract, multiply or divide. Removing a term from one side puts its additive inverse on the other side: 2y + 7 = 21 becomes 2y = 21 − 7. Removing a factor from one side divides the other side by that factor: 2y = 14 becomes y = 14 ÷ 2. Removing a divisor multiplies the other s
- .1 Find the Unknowns
- Matchstick Pattern
- .2 Solving Equations Systematically
- Solving Problems
- Generating Equations
- .3 Mind the Mistake, Mend the Mistake
- .4 A Pinch of History
- Puzzle page
Quick revision
| Idea | What it says | Example from the chapter | Result |
|---|---|---|---|
| Equation | Two expressions joined by '=' | 2n + 1 = 99 | LHS = 2n + 1, RHS = 99 |
| Solving | Find the value that makes LHS = RHS | 2n + 1 = 99 | n = 49 |
| Balance rule | Same operation on both sides keeps equality | 11y + (−5) = 61, add 5 to both sides | 11y = 66 |
| Removing a term | Its additive inverse appears on the other side | 2y + 7 = 21 | 2y = 21 − 7 = 14 |
| Removing a factor | Divide the other side by that factor | 2y = 14 | y = 14 ÷ 2 = 7 |
| Removing a divisor | Multiply the other side by that divisor | u ÷ 15 = 6 | u = 6 × 15 = 90 |
| Unknowns on both sides | Move them to one side first | 6y + 7 = 4y + 21, subtract 4y | 2y + 7 = 21, so y = 7 |
| Trial and error | Substitute values till LHS = RHS | 5x − 4 = 7 | x = 11/5 — guessing is slow here |
| Framing an equation | Name the unknown, then write the fact | ₹25 a plate + ₹50 delivery = ₹500 | 25p + 50 = 500, p = 18 |
| No solution | Two sides can never be equal | x + 4 = x + 5 | No value of x works |
| Brahmagupta's rule | For Ax + B = Cx + D | 650m + 4000 = 500m + 5050 | m = (5050 − 4000) ÷ (650 − 500) = 7 |
| Checking | Substitute the answer back | x = 11/5 in 5x − 4 | 11 − 4 = 7 = RHS ✓ |
Exercises
- .1 Find the Unknowns — In-text Questions Page 164 – 1657
- .1 Find the Unknowns — Math Talk Page 1657
- .1 Find the Unknowns — In-text Questions Page 165 – 1667
- Matchstick Pattern — In-text Questions Page 166 – 167
- .1 Find the Unknowns — In-text Questions Page 1687
- .2 Solving Equations Systematically — Math Talk Page 1687
- .2 Solving Equations Systematically — In-text Questions Page 169 – 1707
- .2 Solving Equations Systematically — In-text Questions Page 170 – 1727
- .2 Solving Equations Systematically — Figure it Out Page 1727
- .2 Solving Equations Systematically — In-text Questions Page 1737
- Solving Problems — In-text Questions Page 174 – 175
- Solving Problems — In-text Questions Page 175 – 177
- Solving Problems — In-text Questions Page 177 – 179
- Generating Equations — Math Talk Page 179 – 180
- Generating Equations — In-text Questions Page 180
- .2 Solving Equations Systematically — Figure it Out Page 1817
- .3 Mind the Mistake, Mend the Mistake — Mind the Mistake, Mend the Mistake Page 181 – 1827
- .4 A Pinch of History — In-text Questions Page 183 – 1847
- .4 A Pinch of History — Figure it Out Page 185 – 1897
- Puzzle page — A Magic Trick Page 190