Equation
An equation is a mathematical statement that two things are equal.
It consists of two expressions, one on each side of an 'equals' sign.
For example:
This equation states that 12 is equal to the sum of 7 and 5, which is obviously true. In an equation, the left side is always equal to the right side.
Using variables
The most common equations contain one or more variables. If we let x
stand for an unknown number, and write the equation
We know the left side and right side are equal, so we can see that x must be 12+5 or 17.
This is the only value that x can have that makes the equation a true statement.
We say that x=17 'satisfies' the equation.
This process of finding the value of the unknowns is called "solving the equation".
We often say that we "solve for x"  meaning solve the equation to find the value of the unknown number
x.
A common mistake
You will often see things that are called equations when they are not. For example you may see something like this
referred to as an equation:
It does not have an equals sign in it, and so is not an equation. It is an expression.
Algebra
The study of algebra is in large part about learning ways to solve various kinds equations. For example, there are ways to solve
quadratic equations such as
A circle can be defined as the locus of all points that satisfy an equation derived from the Pythagorean Theorem. Intercative coordinate geometry applet.
Definiton of the equation of a straight line, in 'point  slope' form: y = m(xPx) + Py
Definiton of the equation of a straight line, in 'slope and intercept' form: y = mx+b
An ellipse can be defined as the locus of all points that satisfy an equation derived from the Pythagorean Theorem. Interactive coordinate geometry applet.
A circle can be defined as the locus of all points that satisfy an equation derived from the Pythagorean Theorem. In this general version, the center of the circle can be anywhere. Interactive coordinate geometry applet.
A circle can be defined as the locus of all points that satisfy an equation derived from Trigonometry. Interactive coordinate geometry applet.
An ellipse can be defined as the locus of all points that satisfy an equation derived from Trigonometry. Interactive coordinate geometry applet.
(C) 2009 Copyright Math Open Reference. All rights reserved
