Finding the Unknown - A Pinch of History

The word 'Algebra' is derived from the title of the book 'Al-Kitab al-mukhtasar fi hisab al-jabr wa’l-muqabala' written by the Persian mathematician Al-Khwarizmi. 'Al-Jabr' means the restoration of broken parts.

Indian mathematicians like Aryabhata and Brahmagupta used 'Beejganit' to refer to algebra. They developed methods to solve linear equations of the form $ax + b = c$.

An algebraic equation is a condition on a variable. It says that two expressions are equal. For example, in $4x + 5 = 25$, the Left Hand Side (LHS) is $4x + 5$ and the Right Hand Side (RHS) is $25$.

Balancing Method: An equation remains unchanged if the same number is added to or subtracted from both sides, or if both sides are multiplied or divided by the same non-zero number.

Transposition Method: Moving a term from one side of the equation to the other is called transposition. During transposition, the sign of the term changes: $+$ becomes $-$, $-$ becomes $+$, $\times$ becomes $\div$, and $\div$ becomes $\times$.