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Algebra Help

Need some algebra help? Or just wanting to review some key concepts in algebra? Here are some lessons to get you started on this important branch of math. With these lessons, algebra will no longer be a mystery reserved for the selected few.

An overview of algebra word problems (includes videos and step by step solutions) covers the common types of word problems in high school and college prep math and the various techniques for solving them.

Free Algebra Worksheets are available to provide practice on some of the following topics, for example solving of equations.

Algebra Topics

Types Of Algebra Word Problems

How to Translate Words to Equations?

The following examples, solutions & videos will show you how to solve the types of algebra word problems that are commonly found in algebra assignments, homework & tests. We hope that these examples will help you learn how to approach the different types of algebra word problems.

Coordinate Geometry & Graphs

A series of Mathematics Lessons given in videos by Portland Community College - Algebra Review

  • Algebraic Expressions & Equations
    Expressions & Equations
    Introduction to Algebraic Expressions:
    What is an algebraic expression?
    The vocabulary of algebraic expressions
    The geometry of algebraic expressions
    Combining like terms
    Simplify Algebraic Expressions using the distributive property

    An introduction to equations:
    Why do we write equations?
    What is an equation? What is a solution to an equation?
    Different types of equations
    Introduction to linear equations:
    What makes an equation linear?
    Using addition property and multiplication property of equality to solve linear equations.
    Checking solutions.
  • Linear Equations & Inequalities
    Equations & Inequalities
    Solve Linear Equations:
    Properties of equality Equations that involve simplification
    Equations containing fractions.
    A general strategy for solving linear equations
    Solution Sets:
    Solutions vs solution sets: graphing solution sets
    Identity equations & inconsistent equations; the empty set; the set of real numbers
    Solution sets for linear equations
    Solutions & solution sets to inequalities; set builder notation

    Solve linear inequalities that have only one variable:
    Solution sets to inequalities.
    The addition property of inequalities
    The positive multiplication property of inequalities
    The negative multiplication property of inequalities
  • Literal Equations, Percents & Mixtures
    Word Problem, Percents, Mixtures
    Literal Equations:
    Solve for a variable
    Modeling & solving word problems using algebra
    Word problems with one unknown
    Word problems with more than one unknown
    An alternative strategy for thinking through the problem

    Working with percents:
    Percents, fractions & decimals
    A basic blueprint for percent questions
    A bona-fide application involving percents

    Problem Solving Mixtures & solutions:
    The fundamental concept of mixing it up in mixture problems.
  • Ratio & Geometry
    Ratio & Geometry
    Ratio, proportions & rates:
    Ratio, rates & rational numbers, Proportions
    Problem Solve with Proportions:
    Direct proportions
    Inverse or reciprocal proportions
    Proportions in geometry

    2-dimensional geometry: Introduction to perimeter & area
    Perimeter, circumference & linear units
    Area & Square Units.

    3-dimensional geometry
    Introduction to volume & surface area
    Volume & surface area formulas
  • Equations & Slopes
    Equations & Slopes
    Equations with two variables:
    Solutions sets to equations with one variable
    Solution sets to linear inequalities with one variable
    Solution sets to equations with two variables

    Plotting solutions from a table:
    Table of values, Application

    Slope between two points, Slope of a line
    Positive slope, negative slope, zero slope

    Determining slope from tables:
    Computing "rise over run"" given a table of data
    Determining whether a table of data describes a linear relationship
    Generating a table of data from a verbal description
  • Slopes & Lines
    Slopes & Lines
    Slope Sense:
    Sign on slope
    Magnitude of slope
    Parallel lines

    Comparing slopes:
    Perpendicular lines
    Vertical lines, Horizontal lines
    Summary of slopes

    Graphing Lines using intercepts:
    Three forms of the equation for a line Intercepts
    Standard Form
    Slope-intercept form

    Matters of scale:
    Slippery slope
    Broken scale
  • Linear Equations
    Linear Equations
    Finding equations of lines:
    Given slope & vertical intercept
    Given both intercepts, Applications

    Slope-intercept form:
    Find the equation of a line given the slope & a point on the line
    Applications of linear equations

    Point-slope form of a linear equation:
    Point-slope form
    Finding a linear equation given two points on a line
    Finding a linear equation given a graph of a line
    Applications of Linear Equations
  • Linear Inequalities
    Linear Inequalities
    Linear Inequalities in two variables:
    Linear inequalities of the form x > C
    Linear inequalities of the form y > C
    Linear inequalities of the form y > mx + b
    Applications of Linear Inequalities in two variables

    Course Review & Summary:
    Linear Equations
    Linear Modeling
  • Systems of Equations
    Systems of Equations
    Solve Systems of Linear Equations:
    What is a solution to a Systems of Linear Equations in Two Variables?
    Solve Systems of Linear Equations by Graphing
    Solve Systems of Linear Equations in Two Variables by Substitution
    When is Substitution the best method?
    Special Cases
    Three Common Solution Methods
  • Systems of Equations Applications
    Systems of Equations Applications
    Applications involving Systems of Linear Equations in Two Variables:
    A Word Problem
    Applications involving money

    Geometry, Systems & Substitutions:
    Linear Systems based in Geometry
    Using Substitution to find new formulas from old
  • Polynomials
    What is a polynomial? Definitions
    Evaluating polynomials

    Multiplying Polynomials:
    Multiply monomials
    The distributive property
    Multiply binomials
    Multivariable Product:
    Multiply polynomials by monomials
    Special products, Products involving polynomials with more than two terms

    The geometry of polynomial multiplication: Basic geometry examples & applications
    Perfect square trinomials
  • Exponents
    Three important rules of exponents
    Two important definitions of exponents
    An alternate definition of a polynomial
    Find a strategy that will work for you
    One last exponent rule
  • Scientific Notation
    Scientific Notation
    Powers of ten & place value
    Computations using scientific notation
    Astronomical Calculations
  • Factoring
    An introduction to factoring
    What is factoring?
    The greatest common factor
    Factor out the greatest common factor
    Factor Binomials of the form x2 + bx + c

    Recognizing patterns that emerge from FOIL
    Guess & check, Factor binomials
    Factor Trinomials by grouping
    Factor second-degree trinomial expressions
    Factor multivariable trinomial expressions
  • Factor Trinomials
    Factor Trinomials
    Special form factorization Perfect Square Trinomials
    Difference of Squares, Sum or difference of cubes
    Discuss what went wrong in the following ?factorizations?

    Solve Quadratic Equations by Factor
    What is a quadratic equation?
    The zero-product principle
  • Finding square roots
    Finding square roots
    Simplify Square Roots Rationalizing the denominator
    Solve Quadratic Equations using the square root property
    Solution sets to quadratic equations
    Solve Quadratic Equations Using the Quadratic Formula
    What is the quickest method to solve a quadratic equation?
  • Quadratic Equations Applications
    Applications of Quadratic Equations
    Working with formulas
    Modeling with quadratic equations
    Graphs of Parabolas
    The axis of symmetry & the vertex
  • Quadratic Equations
    Modelling with Quadratic Equations
    The Graphing Form of Quadratic Equations in Two Variables
    Applications involving maxima & minima
  • Functions & Review
    Relations, Domain, Range
    Definition of a Function, Function Notation
    Numerical & Graphical Representation of Functions

    Course Review:
    Systems of Equations, Exponents & Square Roots
    Polynomials, Quadratic Equations, Functions
    Questions on Systems of Equations, exponents, square roots, scientific notation, quadratics

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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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