EQUATION

EQUAZIONE

• An equation is a mathematical statement that asserts the equality of two expressions. In modern notation, this is written by placing tha expressions on either side of an equals sign (=), for example:

X + 3 = 5 Asserts that x+3 is equal to 5. the = symbol was

invented by Robert Record (1510-1558), who considered that nothing could be more equal than parallel straight lines with the same length.

• 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 knows are denoted by letters at the beginning, a, b, c, d,… . The process of exspressing the unknows in terms of the knows 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 euations, or system of equations, multiple equations are given with multiple unknows. A solution to the system is an assignment of values to all the unknowns so that all of the equations are true.

• Equations can be classified according to the types of operations and quantities involved. Important types include:

• An algebraic equation is an uquation involving only algebraic exspressions in the unknowns. These are further classified by degree.

• A linear equation is an algebraic equation of degree one.

Letters from the beginning of the alphabet like a, b, c… often denote

constants in the context of the discussion at hand, while letters

from the end of the alphabet, like ..x, y, z, are usually reserved for the variables, a convertion initiated

by Descartes.

• If an equation in algebra is known to be true, the follwing operations may be used to produce another true equation:

1. Any real number can be added to both sides.2. Any real number can be subtracted from

both sides.3. Any real number can be multiplied to both

sides.4. Any non-zone real number van divide both

sides.

REALIZZATO DA:ALBANESE ROSANGELACOVELLA GIUSEPPEGIORDANO ARIANNAORFINO MARIASPINELLI AURORA

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