Equations: Finding the Unknown

An equation is a mathematical statement that two expressions are equal. The goal is usually to find the value (or values) of an unknown variable that makes the statement true. Solving an equation means performing the same operation on both sides — adding, subtracting, multiplying, dividing — until the variable stands alone. It's a process of maintaining balance while progressively simplifying.

4,000 years of problem-solving

Babylonian clay tablets from around 2000 BC contain systems of equations — problems about partitioning grain or calculating the dimensions of a field — solved using methods that are recognisably algebraic, even though they're written in words. Greek mathematician Diophantus of Alexandria wrote Arithmetica around 250 AD, a collection of algebraic problems that introduced syncopated notation (abbreviations rather than full words) as a step toward symbolic algebra. al-Khwārizmī's 9th-century text gave the first systematic approach to solving linear and quadratic equations — complete with geometric proofs of why the methods worked.

Equations are everywhere

Physics runs on equations: Newton's second law (F = ma), Ohm's law (V = IR), Einstein's E = mc². Every time a doctor calculates a drug dose based on body weight, they're solving an equation. An engineer checking that a beam can carry a load solves an inequality. A plumber calculating pipe diameters, a chef scaling a recipe, a navigator plotting a course — all are using equations. Even splitting a restaurant bill equally among a group is equation-solving, you're just doing it mentally.