Equations

An equation, in a mathematical context, is generally understood to mean a mathematical statement that asserts the equality of two expressions. In modern notation, this is written by placing the expressions on either side of an equals sign (=), for example

asserts that x+3 is equal to 5. The = symbol was invented by Robert Recorde (1510–1558), who considered that nothing could be more equal than parallel straight lines with the same length.
Centuries ago, the word "equation" frequently meant what we now usually call "correction" or "adjustment". This meaning is still occasionally found, especially in names which were originally given long ago. The "equation of time", for example, is a correction that must be applied to the reading of a sundial in order to obtain mean time, as would be shown by a clock.
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Knowns and unknowns
Equations often express relationships between given quantities, the knowns, and quantities yet to be determined, the unknowns. By convention, unknowns are denoted by letters at the end of the alphabet, x, y, z, w, …, while known's are denoted by letters at the beginning, a, b, c, d, … . The process of expressing the unknowns in terms of the knowns is called solving the equation. In an equation with a single unknown, a value of that unknown for which the equation is true is called a solution or root of the equation. In a set simultaneous equations, or system of equations, multiple equations are given with multiple unknowns. A solution to the system is an assignment of values to all the unknowns so that all of the equations are true.

Analogous illustration

Illustration of a simple equation, x, y, z are real numbers, analogous to weights.
The analogy often presented is a weighing scale, balance, seesaw, or the like.
Each side of the balance corresponds to each side of the equation. Different quantities can be placed on each side; if they are equal the balance corresponds to an equality (equation), if not then an inequality.
In the...