The document discusses equations and their properties. It defines an equation as a mathematical statement asserting the equality of two expressions, with unknown quantities denoted by letters at the end of the alphabet and known quantities by letters at the beginning. Equations can express relationships between knowns and unknowns, and solving an equation means expressing the unknowns in terms of the knowns. Types of equations include algebraic equations, which involve only algebraic expressions in unknowns, and linear equations, which are algebraic equations of degree one.

2. • 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.

3. • 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.

4. • 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.

5. 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.

6. • 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.

7. REALIZZATO DA:
ALBANESE ROSANGELA
COVELLA GIUSEPPE
GIORDANO ARIANNA
ORFINO MARIA
SPINELLI AURORA