# Equations: common information

*Equality. Identity. Equation (unknowns, roots*

of an equation, solving). Equivalent equations.

of an equation, solving). Equivalent equations.

**
Equality
**
- two expressions (numerical or literal ones), jointed by sign " = ".

**- a valid numerical equality or a literal equality, valid at**

*Identity**any*numerical values of letters, contained in it.

E x a m p l e s : 1) A numerical equality 4 · 7 + 2 = 30 is an identity.

2) A literal equality (

*a + b*)(

*a – b*)

*= a*

^{ 2 }

*– b*

^{ 2 }is an identity,

because it is valid at

*all*values of letters, contained in it.

**
Equation
**
– a literal equality, which is valid ( i.e. it becomes an identity ) only at

*some*values of letters, contained in it. These letters are called

**and the values, at which an equality is valid –**

*unknowns*

*roots of an equation.**Procedure of finding*

*all*roots of an equation is called

*solving.**To solve an equation means to find all*

*its roots.*Substitution of each root into an equation instead of unknown converts it into a

*valid numerical equality*(

*identity*). Two or some equations are called

**, if they have the**

*equivalent equations**same roots*.

E x a m p l e : Equations 5

*x –*25

*= 0 and 2*

*x –*7 = 3 are equivalent, because

they have the same root:

*x*=

*5 .*