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.
Forming equations from situationsEquations, LHS and RHSSolving equations by balancing both sidesEquations with the unknown on both sidesWord problems and the history of algebra
Key terms
Equation
A statement of equality between two algebraic expressions.
LHS and RHS
The Left Hand Side and Right Hand Side of an equation, separated by the equals sign.
Solving an equation
Finding the value of the unknown that makes the LHS equal to the RHS.
Inverse operations
Operations that undo each other: addition/subtraction and multiplication/division.
Balance principle
Doing the same operation on both sides keeps the equation balanced.
Trial and error method
Guessing values for the unknown until the equation is satisfied.
Extra questions & answers
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An equation is a statement of equality between:
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