Algebra

Algebra is a branch of mathematics that uses mathematical statements to describe relationships between things that vary over time. These variables include things like the relationship between supply of gasoline and its price. When we use a mathematical statement to describe a relationship, we often use letters to represent the quantity that varies, since it is not a fixed amount. These letters and symbols are referred to as variables.

Variables

A variable is a symbol that represents a number. Usually we use letters such as n, t, or x for variables.

Numerical Coefficient

The numerical part of the term, or the number factor of the term, is what we refer to as the numerical coefficient. This numerical coefficient will take on the sign of the operation in front of it.

Expressions

An expression is a mathematical statement that may use numbers, variables, or both.

Equations

An equation is a statement that two numbers or expressions are equal. Equations are useful for relating variables and numbers.

Terms with the same variables raised to exactly the same powers are like terms.

To combine like terms, add the numerical coefficients and multilpy the result by the common variable factor.

A linear equation in one variable can be written in the form ax + b = c where a, b, c are real numbers and

Equivalent equations are equations that have the same solution.

Addition Property of Equality

Adding the same number to or subtracting the same number from both sides of an equation does not change its solution.

Multiplication Property of Equality

Multiplying both sides or dividing both sides of an equation by the same nonzero number does not change its solution.