Mind the Mistake, Mend the Mistake

Class 7 Maths · Chapter 15: Finding the Unknown · NCERT Ganita Prakash section P2 7.3–7.4

Learn

Neel solves 7 − 8z = 5 and writes "−8z = 5 + 7 = 12". Mistake! To remove the 7 he must subtract 7 from both sides: −8z = 5 − 7 = −2, so z = 1/4. Check: 7 − 8 × 1/4 = 7 − 2 = 5 ✓. Checking catches most mistakes.

7 − 8z = 5 → −8z = −2 → z = 1/4

Common slips: dividing only one side; subtracting the coefficient instead of dividing (3x = 12 does not give x = 9); forgetting to multiply every term inside a bracket (2(x + 5) = 2x + 10, not 2x + 5); and losing a minus sign when moving a term.

A pinch of history: in India, algebra was called bījagaṇita: like a tree hidden in a seed (bīja), the answer hides in an unknown. Brahmagupta (628 CE) wrote rules for working with unknowns, which he named yā, kā, nī …; 2x + 1 was written "yā 2 rū 1". These ideas reached Al-Khwarizmi (around 825 CE), whose book on al-jabr gave us the word algebra.

2x + 1 → yā 2 rū 1

Bhāskarāchārya's horses (1150 CE): one man has ₹300 and 6 horses; another has 10 horses and a debt of ₹100. They are equally rich. With x for a horse's price: 300 + 6x = 10x − 100, so 400 = 4x and x = 100. Brahmagupta's formula: Ax + B = Cx + D has the solution x = (D − B) ÷ (A − C). For 650m + 4000 = 500m + 5050: m = 1050 ÷ 150 = 7.

x = (D − B) ÷ (A − C)

Explore: the steps in order.

1. Put the steps of solving 4x + 7 = x + 22 in order.

Remember

• Check every solution by putting it back into the equation.
• Watch for: one-sided changes, signs, and multiplying every term in a bracket.

Quick check

Which step is wrong? 2(x + 5) = 16 → 2x + 5 = 16 → 2x = 11 → x = 5.5

1. opening the bracket: it should be 2x + 10
2. 2x = 11
3. x = 5.5
4. there is no mistake

Think about it

A giraffe's height is 2.5 m more than half its height. How tall is it?

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.