Chapter 7: Finding the UnknownClass 7 Mathematics — summary, notes, extra questions & MCQ quiz

Summary

This chapter teaches you to form and solve linear equations in one unknown. An equation is a statement of equality between two algebraic expressions, such as \(2n + 1 = 99\); solving it means finding the value of the letter-number that makes the LHS equal to the RHS. Starting from balance-scale puzzles, you learn the central principle: performing the same operation on both sides keeps the equation balanced. So you isolate the unknown by adding or subtracting the same term, and multiplying or dividing both sides by the same number, treating addition/subtraction and multiplication/division as inverse operations. You solve equations with the unknown on one side and on both sides (e.g. \(6y + 7 = 4y + 21\)), always checking the solution by substitution. Real problems — saving money, party costs, marble-sharing, math tricks — are modelled as equations and solved. The chapter closes with a rich history of algebra (bijaganita): Aryabhata, Brahmagupta's general formula \(x = \dfrac{D - B}{A - C}\) for \(Ax + B = Cx + D\), and how the word "algebra" came from al-Khwarizmi's al-jabr.

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