Solving Equations Systematically

Class 7 Maths · Chapter 15: Finding the Unknown · NCERT Ganita Prakash section P2 7.2

Learn

Trial and error works but can be slow: for 2n + 1 = 99, try n = 30 (61, too small), 50 (101, too big), 49 (99 ✓). Undo in reverse order instead. In 4x − 7 = 21, x was multiplied by 4, then 7 was taken away. Undo the last step first: add 7 to both sides, 4x = 28; then divide both sides by 4, x = 7. Check: 4 × 7 − 7 = 21 ✓.

4x − 7 = 21 → 4x = 28 → x = 7

Letters on both sides: k + 8 = 12 − k. Add k to both sides: 2k + 8 = 12; subtract 8: 2k = 4; so k = 2. And 7m = m − 3: subtract m, 6m = −3, m = −1/2. Solutions can be negative or fractions.

k + 8 = 12 − k → k = 2

Brackets: −3(u + 2) = 2(u − 1) opens to −3u − 6 = 2u − 2. Add 3u: −6 = 5u − 2; add 2: −4 = 5u, so u = −4/5. And if 4k + 1 = 13, then without finding k, 8k + 2 = 2 × (4k + 1) = 26.

8k + 2 = 2(4k + 1) = 26

From words to equations: "Two numbers add to 76 and one is three times the other": x + 3x = 76, so x = 19 and 57. "Meher starts with ₹4000 and saves ₹650 a month; Ishaan starts with ₹5050 and saves ₹500": 4000 + 650m = 5050 + 500m, so 150m = 1050 and m = 7 months. Name the unknown, write the equation, solve, then check in the story.

x + 3x = 76 → x = 19

Explore: same solution?

1. Sort each equation by its solution.

Remember

• Undo the operations in reverse order, doing the same to both sides.
• Collect letter terms on one side and numbers on the other; always check the answer.

Quick check

Solve 13 − z = 8.

1. 5
2. 21
3. −5
4. −21

Think about it

Some children and donkeys have 28 heads and 80 feet. How many of each?

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.