Algebra Help

An overview of algebra word problems (includes video) 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

Introduction

Basic Algebra (includes video)

Basic Algebra Terms Constants, Variables, Coefficients, Terms, Expressions, Equations, Quadratic Equations (includes video)

Number Properties - Commutative property, Associative property, Distributive property

Algebraic Expressions (includes video)

Writing Algebraic Expressions (includes video)

Adding and Subtracting Expressions (includes video)

Multiplying and Dividing Expressions (includes video)

Simplifying Expressions (includes video)

Multiplying Expressions or Expanding Expressions (includes video) 

FOIL Method used to distribute two binomials (includes video)   

Techniques to Solve Equations

Isolate the Variable (Transposition) (includes video)

Combine Like Terms (includes video)

Cross Multiply (includes video)

Solving Linear Equations (includes video)

Solving Equations by Addition or Subtraction (includes video)

Solving Equations by Division, Multiplication or taking the Reciprocal (includes video)

Solving Two-Step Equations (includes video)

Solving Equations By Combining Like Terms (includes video)

Solving Equations with the Variable on Both Sides (includes video)

Solving Algebra Equations by Distributive Property (includes video)

Solving Muti-Step Equations (includes video)

Solving Equations with Absolute Values (includes video)

Solving for a Variable in a Formula (includes video)

Systems of Linear Equations, or Simultaneous Equations

Substitution(includes video)
Addition Method (Opposite-Coefficients Method) (includes video)
Graphing method (includes video)

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Inequalities

Inequalities and the Number Line (includes video)

Operations on Inequalities (includes video)

Solving Single-Step Inequalities by Addition or Subtraction (includes video)

Solving Single-Step Inequalities by Multiplication (includes video)

Solving Single-Step Inequalities by Division (includes video)

Solving Inequalities (includes video)

Graphing Linear Inequalities (includes video)

Compound Inequalities (includes video)

Solving Systems of Linear Inequalities / Simultaneous Linear Inequalities (includes video)

Absolute Value Inequalities (includes video)

Solving Quadratic Inequalities (includes video)

Quadratic Equations

Factoring Quadratic Equations
    Finding Common Factors, (includes video)
    Square of Sum, Square of Difference, Difference of Two Squares,
    Coefficient of x² is 1, (includes video)
    Coefficient of x² is greater than 1 (includes video)

Difference of Squares (includes video)

Square of Sum or Perfect Square Trinomials (includes video)

Completing the Square (includes video)

Quadratic Formula or Quadratic Equation (includes video)

Factoring Trinomials

Factoring Trinomials (includes video)

Factoring Trinomials by GCF (includes video)

Factoring Perfect Square Trinomials (includes video)

Factoring Trinomials by Grouping (includes video)

Factoring Trinomials by Trail and Error - Unfoiling (includes video)

Factoring Trinomials with Two Variables (includes video)

Polynomials

Adding and Subtracting Polynomials (includes video)

FOIL Method used to multiply two binomials (includes video)  

Multiplying Polynomials (includes video)

Dividing Polynomials by Monomials (includes video)

Dividing Polynomials by Long Division (includes video)

Synthetic Division (includes video)

Factoring by Grouping (includes video)

Remainder Theorem (includes video)

Factor Theorem (includes video)

Solving Cubic Equations (includes video)

Binomial Theoerm (includes video)

Rational Expressions

Simplifying Rational Expressions (includes video)

Adding Rational Expressions (includes video)

Subtracting Rational Expressions (includes video)

Multiplying Rational Expressions (includes video)

Dividing Rational Expressions (includes video)

Logarithms

Introduction to Logarithms (includes video)

Solving Logarithmic Functions (includes video)

Common and Natural Logarithms (includes video)

Logarithm Rules or Properties of Logarithms (includes video)

Proof for the Properties of Logarithms (includes video)

Solving Logarithmic Equations (includes video)

Graphs of Logarithmic Functions (includes video)

Functions

Relations and Functions (includes video)

Function Notation (includes video)

Domain and Range of a Function (includes video)

Arithmetic Operations on Functions (includes video)

Composite Functions (includes video)

Inverse of a Function (includes video)

Functions & Composite Functions (includes video)

Types Of Algebra Word Problems

Age Word Problems
Age Problems (includes video)
Age Problems involving a Single Person, (includes video)
Age Problems Involving More Than One Person (includes video)

Average Word Problems
Average Problems (includes video)
Arithmetic Mean, (includes video)
Weighted Average (includes video)
Average Speed (includes video)

Coin Word Problems
Problems involving Coins, (includes video)
Stamp problems
Ticket problems

Consecutive Integer Word Problems
Consecutive Integer Problems (includes video)
Consecutive Integer (includes video)
Consecutive Odd Integer (includes video)
Consecutive Even Integer (includes video)

Digit Word Problems
Simple Digit Problems, (includes video)
Convert Digits to Numbers, Interchanging Digits

Distance Word Problems
Distance Problems (includes video)
Travel at Different Rates (includes video)
Travel in Different Directions (includes video)
Given Total Time (includes video)

Fraction Word Problems
Fraction Problems (includes video)

Geometry Word Problems
Geometry Word Problems (includes video)
Involving Perimeters (includes video)
Involving Areas (includes video)
Involving Angles (includes video)

Integer Word Problems
Involving 2 Unknowns, (includes video)
Involving More Than 2 Unknowns

Interest Word Problems
Interest Problems (includes video)

Lever Word Problems
Lever Problems
With 2 Objects, With More Than 2 Objects

Money Word Problems
Money Word Problems (includes video)

Motion Word Problems
Motion Problems (includes video)

Mixture Word Problems
Mixture Problems (includes video)
Adding to a Solution,
Remove from a Solution,
Replace a Solution,
Mix Items of Different Values

Number Sequence Word Problems
Number Sequence Problems (includes video)
Value of a Particular Term, Pattern of a Sequence

Proportion Word Problems
Proportion Problems (includes video)
Directly Proportional, Inversely Proportional

Ratio Word Problems
Ratio Problems
Two-Term Ratios, (includes video)
Three-Term Ratios

Symbol Word Problems
Symbol Problems (includes video)

Variation Word Problems
Direct Variation Problems (includes video)
Inverse Variation Problems (includes video)
Joint Variation Problems (includes video)

Work Word Problems
Work Problems
Two Persons, (includes video)
More Than Two Persons, (includes video)
Pipes Filling up a Tank

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

Introduction to Algebraic Expressions: What is an algebraic expression?
The vocabulary of algebraic expressions
The geometry of algebraic expressions, Combining like terms
Simplifying 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

Solving 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 and inconsistent equations; the empty set; the set of real numbers Solution sets for linear equations
Solutions and solution sets to inequalities; set builder notation
Solving linear inequalities that have only one variable
Solution sets to inequalities, The addition property of inequalities
The positive and negative property of inequalities
The negative multiplication property of inequalities

Literal Equations – Definition, Solving for a variable
Modelling and 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 and decimals
A basic blueprint for percent questions
A bona-fide application involving percents

Problem solving:: Mixtures and solutions
The fundamental concept of mixing it up in mixture problems, Examples

Ratio, proportions and rates
Ratio, rates and rational numbers, Proportions
Problem Solving with Proportions
Direct proportions, Inverse or reciprocal proportions
Proportions in geometry

2-dimensional geometry Introduction to perimeter and area
Perimeter, circumference and linear units
Three-dimensional geometry
Introduction to volume and surface area
Volume and surface area formulas

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

Slope Sens:e Sign on slope, Magnitude of slope, Parallel lines
Comparing slopes: Perpendicular lines, Vertical lines, Horizontal lines
Summary of slopes
Graphing Linear Equations With Two Variables using intercepts
Three forms of the equation for a line Intercepts
Standard Form, Slope-intercept form
Matters of scale: Slippery slope, Broken scale

Finding equations of lines: Given slope and vertical intercept
Given both intercepts, Applications
Slope-intercept form:
Find the equation of a line given the slope and 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 in two variables
Applications of Linear Inequalities in two variables
Course Review and Summary: Linear Equations
Linear Modelling

Solving Systems of Linear Equations
What is a solution to a Systems of Linear Equations in Two Variables?
Solving Systems of Linear Equations in Two Variables by Substitution
When is Substitution the best method?
Special Cases, Three Common Solution Methods
Applications involving Systems of Linear Equations in Two Variables
A Word Problem, Applications involving money
Linear Systems based in Geometry
Using Substitution to find new formulas from old

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

What is a polynomial? Definitions
Evaluating polynomials
Multiplying monomials, The distributive property, Multiplying binomials
Multivariable Product: Multiplying polynomials by monomials, FOIL
Special products, Products involving polynomials with more than two terms
The geometry of polynomial multiplication:, examples and applications
Perfect square trinomials

Scientific Notation: Powers of ten and place value
Computations using scientific notation, Astronomical Calculations

An introduction to factoring: What is factoring?
The greatest common factor, Factoring out the greatest common factor
Factoring Binomials of the form x² + bx + c
Recognizing patterns that emerge from FOIL
Guess and check, Factoring binomials
Factoring Trinomials by grouping
Factoring second-degree trinomial expressions
Factoring multivariable trinomial expressions

Special form factorization, Perfect Square Trinomials
Difference of Squares, Sum or difference of cubes
Discuss what went wrong in the following “factorizations”
Solving Quadratic Equations by Factoring
What is a quadratic equation?
The zero-product principle

Finding square roots Simplifying Square Roots Rationalizing the denominator
Solving Quadratic Equations using the square root property
Solution sets to quadratic equations
Solving Quadratic Equations Using the Quadratic Formula
What is the quickest method to solve a quadratic equation?

Applications of Quadratic Equations
Working with formulas
Modelling with quadratic equations
Graphs of Parabolas
The axis of symmetry and the vertex

Modelling with Quadratic Equations
The Graphing Form of Quadratic Equations in Two Variables
Applications involving maxima and minima

Functions: Relations, Domain, Range
Definition of a Function, Function Notation
Numerical and Graphical Representation of Functions

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

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