Literal EquationsEquations with several variables (letters) are called literal equations.Your job, usually, will be to solve the equation for one of the variables. The letters that do not represent your desired variable move to the other side of the equa…

Direct VariationWhen two variable quantities have a constant (unchanged) ratio, their relationship is called a direct variation. It is said that one variable “varies directly” as the other.The constant ratio is called the constant of variation.The formul…

Solving Linear Systems Algebraically Using SubstitutionThe substitution method is used to eliminate one of the variables by replacement when solving a system of equations.Think of it as “grabbing” what one variable equals from one equation and “plugging…

PercentsPercents are used to describe parts of a whole base amount. When one of the parts of the relationship is unknown, we can solve an algebraic equation for the unknown quantity. (The solution methods shown on this page are of an algebraic, sentence…

Algebraic TranslationsIn the lesson on Algebraic Representations we looked at writing mathematical expressions. We are ready now to write mathematical equations. The word “terms” refers to values that are added or subtracted. 7n + 2 has two terms. The w…

Algebraic RepresentationSolving problems in algebra depends on your ability to represent missing or unknown quantities. Representing unknown quantities is easy to do if you know the “language”.For example, what operation is meant by the phrase more than…

Equations and GraphingThere are several ways to graph a straight line given its equation. The basic method of graphing a straight line is to prepare a table (or T-chart) of x-values and y-values to obtain points, and to plot these points. When dealing w…

Solving Linear Systems Algebraically Using Addition/SubtractionSimultaneous equations got you baffled? Relax! You can do it! Think of the adding or subtracting method as temporarily “eliminating” one of the variables to make your life easier.The goal of …

Rational and Irrational NumbersBoth rational and irrational numbers are real numbers. This Venn Diagram shows the relationships between sets of numbers. Notice that rational and irrational numbers are contained in the large blue rectangle representing t…

Multiplying by a MonomialMonomials can be multiplied times other monomials, times binomials, times trinomials, and times polynomials in general.Multiplying by a monomial may involve: applying rules for dealing with exponentsusing the distributive proper…