What is financial infrastructure?

The network of banks, payment systems and stock markets that helps manage money

What are the main things a bank does?

Holds deposits and lends money as loans

How do banks make money?

They pay lower interest on deposits and charge higher interest on loans

Earning interest on previous interest as well as on the original amount

Solve \(2n + 1 = 99\).

Subtract 1: \(2n = 98\); divide by 2: \(n = 49\).

Solve \(5x - 4 = 7\).

Add 4: \(5x = 11\); divide by 5: \(x = \dfrac{11}{5}\).

Solve \(6y + 7 = 4y + 21\).

Subtract \(4y\): \(2y + 7 = 21\); then \(2y = 14\), so \(y = 7\).

Why should you check a solution?

Substituting it back should make the LHS equal the RHS, confirming correctness.

Where does the word "algebra" come from?

From al-jabr in al-Khwarizmi's book "Hisab al-jabr wal-muqabala".

Finding the Unknown

Q: What is an equation?

A statement of equality between two algebraic expressions, e.g. \(2n + 1 = 99\).

Q: What is the key principle for solving equations?

Performing the same operation on both sides keeps the equation balanced.

Class 7 Mathematics · Ganita Prakash Part 2 · Chapter 7

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Five congruence conditions to equations

Marks booster + cheatsheet: key concepts in 2 lines each
Integer sign rules, Ch 2
HCF and LCM by prime factors, Ch 3
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Mean, median and outliers, Ch 5
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CBSE Class 7 · Mathematics

8 chapters: lakhs and crores to fractions

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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.

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

Try one from this chapter

An equation is a statement of equality between:

Flashcards & interactive practice