# Expressions and Equations Relevant Notes

Relevant Vocabulary

Variable (description): A variable is a symbol (such as a letter) that represents a number, i.e., it is a placeholder for a
number.

Numerical Expression (description): A numerical expression is a number, or it is any combination of sums, differences,
products, or divisions of numbers that evaluates to a number.

Value of a Numerical Expression: The value of a numerical expression is the number found by evaluating the expression.

Expression (description): An expression is a numerical expression, or it is the result of replacing some (or all) of the
numbers in a numerical expression with variables.

Equivalent Expressions: Two expressions are equivalent if both expressions evaluate to the same number for every
substitution of numbers into all the letters in both expressions.

An Expression in Expanded Form: An expression that is written as sums (and/or differences) of products whose factors
are numbers, variables, or variables raised to whole number powers is said to be in expanded form. A single number,
variable, or a single product of numbers and/or variables is also considered to be in expanded form. Examples of
expressions in expanded form include: 324, 3x, 5x + 3 − 40, x + 2x + 3x, etc.

Term (description): Each summand of an expression in expanded form is called a term. For example, the expression
2x + 3x + 5 consists of 3 terms: 2x, 3x, and 5.

Coefficient of the Term (description): The number found by multiplying just the numbers in a term together. For
example, given the product 2 ∙ x ∙ 4, its equivalent term is 8x. The number 8 is called the coefficient of the term 8x.

An Expression in Standard Form: An expression in expanded form with all its like terms collected is said to be in
standard form. For example, 2x + 3x + 5 is an expression written in expanded form; however, to be written in standard
form, the like terms 2x and 3x must be combined. The equivalent expression 5x + 5 is written in standard form.