Fundamental Concepts of Algebra and Equations

Fundamental Concepts in Algebra

Numerical Language

Expressing mathematical information using only numbers.

Algebraic Language

Expressing mathematical information using both numbers and letters.

Algebraic Expression

A set of numbers and letters combined with mathematical operation signs.

Numerical Value of an Algebraic Expression

The number obtained by replacing the letters with their corresponding values and performing the indicated operations.

Monomial

A monomial consists of a number and one or more letters:

• The number (including its sign) is called the coefficient.
• The letter or letters that accompany it are called the literal part.

Degree of a Monomial

The sum of the exponents of the letters that form it.

Similar Monomials

Two or more monomials are similar if they have the same literal part (i.e., the letters).

Equality

Consists of two expressions separated by the equals sign (=). According to their expressions, they can be:

• Numerical: When only numbers are involved.
• Algebraic: When numbers and letters are involved.

Identity

An algebraic equality that is true for any value of the letters.

Equation

An algebraic equality that is only true for some values of the letters.

Members of an Equation

The algebraic expressions on either side of the equality sign.

Terms of an Equation

The addends that constitute the members.

Unknowns of an Equation

The letters that appear in those terms, whose values are unknown.

Degree of an Equation

The highest degree of its terms.

Solution of an Equation

The numerical values of the unknowns that make the equality true.

Equivalent Equations

Two equations are equivalent when they have the same solution.

Solving an Equation

The process of finding its solution.