Algebra Help

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 Help
Algebra Topics	Algebra Word Problems	Coordinate Geometry & Graphs
Algebra Review	Algebra Worksheets	Math Worksheets

Algebra Topics

• Introduction

  Basic Algebra
  An introduction to Algebra
  
  Basic Algebra Terms
  Constants, Variables, Coefficients, Terms, Expressions, Equations, Quadratic Equations
  
  Number Properties
  Commutative property, Associative property, Distributive property
  
  Algebraic Expressions
  Variables, constants, terms, expressions, & coefficients
  
  Write Algebraic Expressions
  Translate from words to algebraic expressions.
  
  Add & Subtract Expressions
  Multiply & Divide Expressions
  Simplify Expressions
  Multiply Expressions or Expand Expressions
  FOIL Method used to distribute two binomials

• Techniques To Solve Equations

  Isolate the Variable (Transposition)
  Combine Like Terms
  Cross Multiplication
  
  Solve Linear Equations
  Solve Equations by Addition or Subtraction
  Solve Equations by Division, Multiplication or taking the Reciprocal
  Solve Equations by Combining Like Terms
  Solve Equations with Variables on Both Sides
  Solve Algebra Equations by Distributive Property
  
  Solve Two-Step Equations
  Solve Multi-Step Equations
  Solve Equations with Absolute Values
  Solve for a Variable in a Formula

• Systems Of Linear Equations, Or Simultaneous Equations

  Solve Systems of Equations: Substitution
  Solve Systems of Equations: Addition Method (Opposite-Coefficients Method)
  Solve Systems of Equations:Graphically

• Inequalities

  Inequalities & the Number Line
  Operations on Inequalities
  
  Solve Single-Step Inequalities by Addition or Subtraction
  Solve Single-Step Inequalities by Multiplication
  Solve Single-Step Inequalities by Division
  
  Solve Inequalities
  Graphing Linear Inequalities
  Compound Inequalities
  Solve Systems of Linear Inequalities / Simultaneous Linear Inequalities
  
  Absolute Value Inequalities
  Solve Quadratic Inequalities

• Factor & Solve Quadratic Equations

  Factor Quadratic Equations
  Finding Common Factors
  Square of Sum
  Square of Difference
  Difference of Two Squares
  
  Coefficient of x² is 1
  Coefficient of x² is greater than 1
  Difference of Squares
  Square of Sum or Perfect Square Trinomials
  
  Completing the Square
  Quadratic Formula or Quadratic Equation
  Graphical Solutions of Quadratic Equations
  How the solutions of a quadratic equation is related to the graph of the quadratic function, how to use the graphical method to solve quadratic equations.

• Factor Trinomials

  Factor Trinomials
  Factor Trinomials by GCF
  Factor Perfect Square Trinomials
  Factor Trinomials by Grouping
  Factor Trinomials by Trail & Error - Unfoiling
  Factor Trinomials with Two Variables

• Polynomials

  Add & Subtract Polynomials
  FOIL Method Used To Multiply Two Binomials
  Multiply Polynomials
  Divide Polynomials by Monomials
  Divide Polynomials by Long Division
  
  Synthetic Division
  Factor by Grouping
  Remainder Theorem
  Factor Theorem
  Solve Cubic Equations
  Binomial Theorem

• Rational Expressions

  Simplify Rational Expressions
  Add Rational Expressions
  Subtract Rational Expressions
  
  Multiply Rational Expressions
  Divide Rational Expressions
  Partial Fraction Decomposition

• Logarithms

  Introduction to Logarithms
  Solve Logarithmic Functions
  Common & Natural Logarithms
  Logarithm Rules or Properties of Logarithms
  
  Proof for the Properties of Logarithms
  Solve Logarithmic Equations
  Graphs of Logarithmic Functions

• Functions

  Relations & Functions
  Function Notation
  Domain & Range of a Function
  
  Arithmetic Operations on Functions
  Composite Functions
  Functions & Composite Functions
  Inverse of a Function

• Real Number

  Add & Subtract Real Numbers
  Multiply & Divide Real Numbers
  Properties of Real Numbers
  Identity Property of 1 & 0
  Order of Operations for Real Numbers

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.

• Age Word Problems

  Age Problems
  Age Problems: Single Person
  More Than One Person
  Age Word Problems 1
  Age Word Problems 2

• Average Word Problems

  Arithmetic Mean
  Weighted Average
  Average Speed

• Coin Word Problems

  Problems involving Coins
  Stamp Problems
  Ticket Problems
  Coin Word Problems 1
  Coin Word Problems 2

• Consecutive Integer Word Problems

  Consecutive Integers 1
  Consecutive Integers 2
  Consecutive Odd Integer
  Consecutive Even Integer

• Digit Word Problems

  Simple Digit Problems
  Convert Digits To Numbers & Interchanging Digits
  Digits Word Problems

• Distance Word Problems

  Travel in Same Direction
  Travel in Opposite Directions
  Round Trip Problems
  Average Speed Problems
  Wind/Current Problems

• Fraction Word Problems

  Algebra Problems That Involve Fractions

• Geometry Word Problems

  Geometry Word Problems
  Involving Perimeters
  Involving Areas
  Involving Angles
  Volume Word Problems
  
  Perimeter Word Problems 1
  Perimeter Word Problems 2
  Area Word Problems
  Angle Word Problems

• Integer Word Problems

  Involving 2 Unknowns
  More Than 2 Unknowns
  Integer Word Problems 1
  Integer Word Problems 2

• Interest Word Problems

  Interest Problems
  Simple Interest Word Problems
  Compound Interest Word Problems
  Compound Interest & Continuously Compound Interest
  Investment Word Problems

• Lever Word Problems

  Involving 2 Or More Objects

• Mixture Word Problems

  Mixture Problems
  Add to a Solution
  Remove from a Solution
  Replace a Solution
  
  Mix Items of Different Values
  Algebra Mixture Problems 1
  Algebra Mixture Problems 2
  Algebra Mixture Problems 3

• Money Word Problems

  Money Word Problems

• Motion & Distance Word Problems

  Motion Word Problems
  Rate, Time, Distance Problems 1
  Rate, Time, Distance Problems 2
  Rate, Time, Distance Problems 3

• Number Sequence Word Problems

  Number Sequence Problems
  Value of a Particular Term
  Pattern of a Sequence

• Proportion Word Problems

  Proportion Problems
  Direct Proportion Problems
  Inverse Proportion Problems
  Proportion Word Problems
  Ratio & Proportion Problems

• Word Problems Using Quadratic Equations

  Quadratic Word Problems
  Geometry Word Problems
  Projectile Motion

• Ratio Word Problems

  Ratio Problems
  Two-Term Ratios
  Three-Term Ratios
  Ratio Word Problems

• Symbol Word Problems

  Symbol Problems

• Variation Word Problems

  Direct Variation Problems
  Inverse Variation Problems
  Joint & Combined Variations

• Work Word Problems

  Work Problems
  Two Persons
  More Than Two Persons
  
  Pipes Filling up a Tank
  Algebra Work Problems 1
  Algebra Work Problems 2

Coordinate Geometry & Graphs

• Coordinate Geometry & Graphs

  Coordinate Geometry
  Coordinate plane, Slope Formula, Equation of a Line, Slopes of parallel lines, Slope of perpendicular lines, Midpoint Formula, Distance Formula
  
  Coordinate Plane
  Coordinate plane or Cartesian plane, points on the Cartesian Plane, quadrants.
  
  Slope of a Line
  Slope of line from the graph (rise over run), using the slope formula, negative slope, y-intercept
  
  Equation of a Line
  Slope-intercept form for the equation of a line, how to write equations in slope-intercept form, how to write equations of horizontal & vertical lines, how to get the equation of a line given two points on the line.
  
  Forms of Linear Equations
  Slope-intercept form, the point-slope form, the general form, the standard form, how to convert between the different forms of linear equations.
  
  Graphing Linear Equations
  How to graph linear equations by plotting points, how to graph linear equations by finding the x-intercept & y-intercept, how to graph linear equations using the slope & y-intercept.
  
  Slope & Intercept of a Linear Equation
  How to graph a linear equation when the equation is given in slope-intercept form or when the equation is given in general form.
  
  Explore the straight line graph Activity to investigate how the change of the slope and y-intercept can affect the straight line graph.
  
  Equation of a Line Parallel to the X-axis or Y-axis
  Equation of a Line Given its Slope and a Point on the Line
  Equation of a Line Given Two Points on the Line
  
  Slopes of Parallel & Perpendicular Lines
  How to determine if two lines are parallel or perpendicular when given their slopes, how to find the equation of a line given a point on the line & a line that is parallel or perpendicular to it, how to find parallel or perpendicular lines using Standard Form.
  
  Midpoint Formula
  Midpoint formula, how to find the midpoint given two endpoints, how to find one endpoint given the midpoint & another endpoint, how to proof the midpoint formula.
  
  Distance Formula
  How to derive the distance formula from the Pythagorean Theorem, how to use the distance formula.

• Linear Inequalities & Linear Programming

  Graphing Linear Inequalities
  Graph of linear inequalities, how to graph linear inequalities, how to graph systems of linear inequalities.
  
  Graphing Inequalities
  
  Linear Programming
  Linear programming, how to use linear programming to solve word problems.

• Functions & Graphs

  Quadratic Functions
  Different forms of quadratic functions, general form, factored form, vertex form, convert from general form to factored form, convert from the general form to the vertex form using the vertex formula, convert from the general form to the vertex form using completing the square.
  
  Graphing Quadratic Functions
  How to graph of quadratic functions by plotting points, how to graph quadratic function of the form y = ax^2, the properties of the graph y = ax², how to graph a quadratic function given in general form, how to graph a quadratic function given in factored form, how to graph a quadratic function given in vertex form.
  
  Graphical Solutions of Quadratic Equations
  How the solutions of a quadratic equation is related to the graph of the quadratic function, how to use the graphical method to solve quadratic equations.
  
  Graphing Cubic Functions
  How to graph of cubic functions by plotting points, how to graph cubic functions of the form y = a(x − h)³ + k.
  
  Graphing Exponential Functions
  How to graph exponential functions by plotting points, the characteristics of exponential functions, how to use transformations to graph an exponential function.

A Series Of Mathematics Video Lessons 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:
  - Definition
  - 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.
  - Examples.

• 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:
  - 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

  Polynomials
  Polynomials:
  - What is a polynomial? Definitions
  - Evaluating polynomials
  
  Multiplying Polynomials:
  - Multiply monomials
  - The distributive property
  - Multiply binomials
  
  Multivariable Product:
  - Multiply polynomials by monomials
  - FOIL
  - Special products, Products involving polynomials with more than two terms
  
  The Geometry Of Polynomial Multiplication: - Basic geometry examples & applications
  - Perfect square trinomials

• Exponents

  Exponents
  Exponents:
  - Three important rules of exponents
  - Two important definitions of exponents
  - An alternate definition of a polynomial
  - Examples
  - 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

  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

  Functions
  - 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

Try the free Mathway calculator and problem solver below to practice various 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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