Archive for February, 2011


Volume of Basic Figures Lesson

Knowing how to find the volume of cubes, cones, spheres and other basic figures is really important for algebra students.  If  you know how to apply the following formulas you will be fine- make sure you use the right units of measure! Some key concepts to remember about area and volume: * area is measured […]

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Solving Two Step Equations

Solving equations that involve two steps is really two basic equations in one problem.  Always do the addition or subtraction part first before solving for the variable using division or multiplication. Key concepts to keep in mind: * understand positive and negative number operations first before doing equations * understand fractions before doing equations * […]

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Solving Systems of Inequalities

Before taking on a system inequality problem you should ask yourself:  can I solve a system?  can I do a basic linear inequality problem? If you answer yes to both of these questions then you should have no problem- systems of inequalities are easy if you have those other skills down.  Below are some notes […]

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Surface Area of Basic Figures Lesson

Finding the surface area of basic figures like cylinders, prisms, pyramids and cones should be no problem if:  you know the right formula and can evaluate the formula correctly.  Big mistakes students make even if they are using the right formula is making order of operation mistakes.  Also make sure you always add the proper […]

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Writing Lines in Standard Form

Writing lines (linear equations) in Standard Form is a must know skill for algebra students.  Often times we see lines in y = mx + b  form (example y= 3x + 7) and this is good if we want to graph a line using the slope-intercept method.  However a line in Standard Form ( Ax + […]

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Polynomial Multiplication Special Rules

Of course when faced with multiplying two polynomials (binomials) you can just use the F.O.I.L. method and call it a day.  However recognizing that you are multiplying binomials with the following pattern (a + b)(a – b),   (a + b)(a + b), (a – b)(a – b) can allow you to break out a […]

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Special Factoring Rules

When recognizing that you are multiplying binomials with the following pattern (a + b)(a – b),  (a + b)(a + b), (a – b)(a – b) you can break out a special multiplication rule to get the product. However the more important benefit to mastering these rules is when you use them in reverse to […]

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Solving Rational Equations

  Solving rational equations involves some very important steps and you really need to know what you’re doing to find the solution.  The good news is your smart, dedicated and a hard worker so you can do these problems!  But lets go over a few details to get you going in the right direction.  First […]

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Solving Radical Equations

Solving radical equations involves some very important steps and you really need to know what you’re doing to find the solution.  The good news is your smart, dedicated and a hard worker so you can do these problems!  But lets go over a few details to get you going in the right direction.  First you […]

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Solve Two Variable Inequalities

Solving two variable inequalities involves graphing a line and shading a portion of the graph that identifies the solution region.  So before you proceed make sure you really know how to graph a line (linear equation).  Next when graphing a line make sure you pay attention to the inequality symbol- this will determine if the […]

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Solving Systems Substitution Method

Knowing how to solve a system of linear equations is an absolute must for algebra students.  There are four basic ways you can solve a linear system: * graphing method ( not really practical – only used to teach the concept of solutions to a system) * substitution method (learn it, love it, don’t forget […]

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Solving Systems Graphing Method

Knowing how to solve a system of linear equations is an absolute must for algebra students.  There are four basic ways you can solve a linear system: * graphing method ( not really practical – only used to teach the concept of solutions to a system) * substitution method (learn it, love it, don’t forget […]

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Solve Linear Inequalities

Don’t you just love inequalities?  Of course I can only hear you saying “not really…inequalities stink!”  Well I know you may not like inequalities but you need to know how to work with them.   All right let me stress some points: * the solution to an inequality is more than a single number;  inequalities […]

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Solve Absolute Value Inequalities

Absolute value inequalities are not quite the same as linear inequalities.  Of course the biggest difference is that absolute value inequalities have an absolute value symbol.   No problem, we can solve these bad boys by rewriting the absolute value inequality in a different way such that it does not have the absolute value part. […]

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Solve Absolute Value Equations

What’s the absolute value of -3?  |-3| = 3  That was easy. How about the absolute value of  3?  |3|=3. Now let’s try this brain teaser, the absolute value of what number is 3?  i.e. |x|=3?   well we already determined above that 3 and -3 both have the absolute value of 3.  Therefore the […]

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Slope of a Line

The slope of a line which is represented by the variable “m” is front and center when it comes to understanding graphs of lines (linear equations).  What is the slope?  It’s simple it’s just the measurement of the angle of the line.  Lines that rise from left to right (like the image below) have positive […]

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Find the Equation of a Line Using The Slope Intercept Formula Lesson

The are a few different ways to find the equation of a line; using the slope-intercept formula is one of the most common.  Remember the formula y = mx + b?  We love lines in this form (y=mx + b ) because it’s very easy to graph them- we just use the slope (m) and […]

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Simplifying Radicals

Ah…the wonderful world of the radical (square root symbol).  Don’t like radicals? Too bad- they are everywhere in algebra and math so chill out and get to love these little rascals.   The first order of business when dealing with radicals is being able to simplifying them.  Just like “simplifying” fractions (reducing  ex.  20 / […]

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Scientific Notation

Scientific notation is a great way to deal with super large or super small numbers.  Lets consider the number 8723500000000000 not really a number I want to put in my pocket and walk around with all day (unless of course it’s money) I prefer numbers that much easier to write and deal with like 8.72. […]

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Ratios Rates and Proportions

Rates, ratios and proportions go together like a cheeseburger, fries and a coke.  So what’s this bond I speak of with these terms?  First let me start by saying rates and ratios are nothing more than fancy fractions (I’ll explain in a second).  Next a proportion is nothing more that an equation involving two equal […]

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Quadratic Formula

Think of the most popular people you know…movie stars, presidents, sports heroes, etc. Well in the world of algebra nothing is more famous than the Quadratic Formula!  All right after that grand introduction what the heck is the quadratic formula?   The quadratic formula is a powerful tool that allows you to find the solution […]

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Solve Quadratic Equations by Square Roots

Often the easiest way to solve a quadratic equation is by taking the square root of both side of the equation (as illustrated below).   Now this method of taking the square roots of  both sides is only practical when it results in getting the variable by itself on one side of the equation.  So […]

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Solve Quadratic Equations by Factoring

I just love factoring!  Now many of you might think “wow this guy has no life..” but nothing could be further from the truth- my life is great!  You see if you can factor especially factor polynomials everything becomes easier.  Ask yourself do you want to work harder or smarter?  Well if your answer is […]

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Quadratic Equations Discriminant

A very interesting part of the quadratic formula is the discriminant.  Specifically the discriminant is the “b squared – 4ac” part of the formula (located under the square root symbol).  This part of the quadratic formula can tell us some useful information about the solutions of the equation.  Remember a quadratic equation will always have […]

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Solve Quadratic Equations Completing The Square

People that make algebra easier are our friends!  Some poor fellow used to solve quadratic equations by completing the square and finally discovered a much easier way- it’s called the quadratic formula!  Yes the completing the square method of solving a quadratic equation is the “long way” – a better, faster way is the quadratic […]

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Pythagorean Theorem

The Pythagorean Theorem is a must know for all algebra students. Just because the Pythagorean Theorem deals with basic geometry it has alot of application in algebra.  One more thing for those of you that will be taking geometry expect to see a lot of algebra.  You will need various algebra skills to solve geometry […]

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Rules of Powers and Exponents

The Rules of Powers and Exponents are sometimes called the “Properties of Exponents” the important thing is no matter what they are called you need to know them to win in the algebra game.  Study the rules below and work hard to master how to use them and watch your test grades rise! Key concepts […]

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Write Equation of Line Point Slope Formula

Writing the equation of a line is a basic skill in algebra. There are a few ways to write the equation of a line but one of the most common ways is to use the point-slope formula.  The key to this and any other formulas is knowing how to plug in the correct values.  My […]

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Solving Percent by Proportions

You can solve percent problems by proportions or equations.  Both ways are good but of course you want to stick with the method you like the best.  However you need to take the time to learn both methods.  If your having problems with this method go back and review ratios and proportions. Key concepts to […]

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Percent

I know you have a good “feel” about percent- everyone should with all the percent ads we see like 50% off  a pair of old socks!  Anyways lets get serious about percent because you need to master the topic to excel at math and algebra- and shopping.  After you learn how to find the percent […]

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Operations with Radicals

“Operations with radicals” is not conducting surgery with a bunch of crazy people. The topic is far more fun it involves dealing with radical operations which are square roots.  Now if your looking to lock up a great grade in algebra you need to master these radicals.  The notes below will help you get a […]

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Multiplying Polynomials

You know how to multiply numbers but that’s no real fun.  If you are looking for a real good time then learn how to multiply polynomials.  Once you have the various methods to multiply polynomials down your algebra life will be wonderful!  Just on a serious note you MUST know polynomial operations to get past […]

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Multiplying and Dividing Rational Expressions

Multiplying and Dividing Rational Expressions- sounds hard but it’s not if you understand a few things.  First rational expressions are fractions that are made of variable expressions.  Next multiplying and dividing rational expressions follow the same steps as multiplying and dividing numbers.  So as you study this topic in algebra go back and make sure […]

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Multiplying and Dividing Fractions

Often it’s the easy things we tend to mess up. This seems to be the case with many students when it comes to dealing with fractions. Multiplying and dividing fractions are easy operations but as I said many students get confused as to what steps to take. When we multiply fractions we simply multiply respective […]

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Mid-Point Formula Lesson

Wow! another formula to remember in algebra- just what you wanted.  However sad you might be at learning more formulas the mid-point formula is pretty easy.  The formula tells you the location (a point) that’s “mid way” between two other points. Like any formula make sure you understand how to plug in the correct values. […]

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Systems Linear Programming

If you were wondering what’s the hardest topic in algebra – linear programming might just be it.  So many students have a difficult time when first learning systems and then to add linear programming to the mix can cause even more problems.  However linear programming is very important in algebra and as hard and complex […]

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Linear and Non-linear Functions

Linear functions, non-linear functions..who cares!  Well if you like good grades in algebra then you want to take “care” on understanding the differences between various functions.  Linear functions are lines and non-linear functions are other shapes like parabolas.  As long as you have a basic idea of the different type of functions you will be […]

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Systems Elimination Linear Combination

Solving systems is a core skill in algebra so you need to get “hard core” about the effort you put into mastering systems.  For the most part you will be using two methods to solve systems- the linear combination method and substitution method.  both methods are great and you need to master them both.  Systems […]

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Function Inverse

The inverse of a function is like a function’s “anti-function”.  To put this another way an inverse function undoes a function.  As you can see below an inverse function’s domain and range are the exact opposite of that of the function.  As an algebra student not only do you want to understand the concept of […]

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Introduction to Functions and Relations

Functions and relations are a HUGE part of algebra!  As such you want to take the time to learn all the terms and language that goes with this most important topic.  Just as a start a relation is a collection of points like (1, 3), (6, 9), (0, 5), etc.  A function is a special […]

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Graphing Quadratic Equations

You thought that all you had to do was learn how to graph lines in algebra? What fun would that be- lines are boring!  So to make algebra interesting we expect students to be able to graph quadratic equations.  Quadratic equations have  U shaped graphs called “parabolas”.  The top or bottom location of this “U” […]

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Graphing Quadratic Inequalities

Take a quadratic equation mix it with an inequality and graph it- the result is a quadratic inequality.  These problems take time so don’t rush to graph these quadratic inequalities because it’s easy to make mistakes.  The key is to first know how to graph a quadratic equation and linear inequality. The notes and example […]

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Graphing Lines y=mx + b (Slope-Intercept Method) Full Video Lesson

The slope-intercept form of a line is the way you will see most lines expressed in algebra.  The form is y=mx + b where m=the slope and b= the y-intercept. For example the line y=3x + 7 has a slope =3 and a y-intercept=7. When graphing lines in slope-intercept form you need to follow two […]

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Graphing Lines Using a Table

Almost any function you encounter in algebra can be graphed by creating a table of values. As such you want to understand how to construct a table of values and use these values to plots points and graph lines.  The key thing to remember is that creating your table involves doing calculations so be very […]

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Graphing One Variable Lines

It’s always the easy things that we tend to mess up.  Welcome to the world of graphing one variable lines.  For many years as a math teacher I have seen students confuse these basic line equations for no other reason they could not remember the simple formulas.  So please take it from me that you […]

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Graphing Lines Using Intercepts Ax + By = C

  Graphing lines using intercepts is easy when lines are in standard form (Ax + By = C).  The intercepts are just the locations where a line crosses the x and y axis.  To find the y intercept we let x=0 and then solve for y.  To find the x intercept we let y=0 and […]

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Basic Inequalities

Come on is there anything “basic” in math? Of course there is and hopefully you will find this introduction to inequalities easy.  A few things to remember.  First inequalities have many (infinite) solutions.  Example lets consider x > 3  or “what numbers x are greater than 3”.  How many numbers can make this statement true? […]

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Graphing Absolute Value Functions

Graphing Absolute Value Functions is an important skill to master in algebra. The key is to remember that each graph has a V shape and the V starts from a point called the vertex.  Also the V shape can be upside down- see below to determine how to identify all the characteristics of an absolute […]

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Functions Vertical Line Test and Mapping

“To be or not to be a function- that is the question”.  So lets say someone is trying to sell you a function and you want to know if it’s fake.  Is this really a function you might ask?  Well to protect yourself from a fraud and bad algebra grades you want to know the […]

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Function Operations

Function operations are a must know for algebra students.  Let’s review what the word “operation” means.  In math an  operation is what you can do to numbers- i.e. add, subtract, multiply or divide.  However operations not only apply to numbers but to a whole range of things to include functions.  So as you will see […]

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Fractions LCM and LCD

Want to add or subtract fractions? Well then you will want to understand the LCM and LCD.  LCM stands for the Least Common Multiple and basically it’s the lowest number that will divide into two or more numbers.  LCD stands for the Lowest Common Denominator and it’s basically the LCM of the denominators when considering […]

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Solving Formula Equations

Solving formula equations or literal equations is not hard if you understand how to solve regular variable equations.  When we are solving a formula equation all we are doing is writing the formula in a different way.  Example, lets consider the formula Area=Base * Height written as A=BH.  Now if I told you to solve […]

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Factoring Quadratic Trinomials

Want to make some extra money tutoring algebra?  Well all you have to do is become an expert in factoring polynomials and you will be the most popular student in town!  All joking aside factoring polynomials especially trinomials is fundamental to do well in algebra.  Stated another way if you can’t factor trinomials your algebra grade […]

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Factoring The GCF from a Polynomial

In algebra when we factor a polynomial we always start with the GCF( greatest common factor). I know you might have some fancy algebra factoring skills but don’t apply any of them in a factoring problem until you find the GCF.  Sometimes a polynomial will not have a gcf so in those cases use your […]

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Exponential Growth and Decay

Exponential growth and decay is just a description on how something grows or decays overtime. Example, lets say you have two rabbits and they have babies and their babies have babies and so forth- it wont be long until you have a backyard full of rabbits- can you say Bugs Bunny!  This kind of “explosive” […]

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Evaluate Absolute Value

Evaluating an absolute value expression is when you calculate the value of the problem. Remember when you find the absolute value of a number the answer is always positive. However when absolute values are apart of a larger expression the overall value can be any real number- positive or negative. Key concepts to remember: * […]

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How to Find The Equation of a Line

So you want to know how to find the equation of a line.  This is a skill you must know as an algebra student.  Before I explain the steps to find the equation of a line I like to stress that we like to write all linear equations (line equations) in the form y=mx + […]

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Distance Formula

Put away the tape measure- if you want to find the distance between two points (x, y) we can break out the “distance formula”. The formula relates to geometry but it’s huge in algebra.  The formula is pretty easy to use and although it looks a little complex it’s really not.  Let’s say I want […]

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Direct and Inverse Variation

One nice little topic you will study as an algebra student is variation.  The concept takes a look at how variables relate to one another in equations and especially in formulas.  There are a few different types of variation you need to know but I want to focus on direct and inverse variation. Let’s explore […]

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Convert Fractions and Decimals

Got a calculator? Then let’s travel to the land of fractions and decimals.  To be clear never think that a calculator is a way out of getting out of knowing what you are doing!  As a math teacher I can’t tell you how many students trusted their calculators only to discover the pain of a […]

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Compound Interest

Free Money!  Yes indeed if you understand a little something about compound interest. A quote from Albert Einstein: “The most powerful force in the universe is compound interest” Compound interest is a description of how something grows overtime and you need to understand it as an algebra student.  An easy way to describe compound interest […]

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Composite Functions

The function operation that most algebra students dislike is the composite function.  However once algebra students learn to handle these problems they warm up to the topic.  A composite function is nothing more than evaluating a function with another function.  Lets take take the function f(x)=3x + 1.  If I said evaluate the function for […]

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Best Fitting Lines And Scatter Plots

Good news! Sometimes in algebra you get to guess- well not totally but kind of.  Finding the “best fitting line” is an example when we estimate the best line that over laps a trend of points on a graph. What you do is use your best judgment to find a set of points ( 2 […]

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Area and Circumference of Circles Lesson

Area and Circumference are must knows for your study of circles. Keep in mind that the value of pi can be estimated around 3.14 or 22/7 as a fraction. Many students make errors using these formulas because they are weak with the order of operations so if you are having problems double check your understanding […]

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Area of Basic Figures Lesson

Finding the area of basic figures to include triangles and rectangles are a must know for algebra students. Remember that you will be using formulas so watch out for errors with the order of operations, positive and negative numbers and powers. Some key concepts to remember about area and volume: * area is measured in […]

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Adding and Subtracting Polynomials

Mastering polynomials is essential to your success in algebra.  As you progress into more complex college prep math you will find polynomials will get even more attention- they just love the being seen like a movie star.  Anyways adding and subtracting polynomials is easy if you know how to add like terms.  For the most […]

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Adding and Subtracting Rational Expressions

If you thought fractions were hard you will hate adding and subtracting rational expressions.  But lets be positive, that was before you came to algebratesthelper.com I got your back- everything is going to be lovely.  Ok first off a rational expression is a fraction that has variables.  So what we are doing here is adding […]

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Adding and Subtracting Fractions

Fractions the most loved of numbers in algebra- NOT!  I know most of you hate fractions but get over it you need to master and love these most important numbers.  Many students think they can just use their calculator in algebra and not deal with the headaches of fractions.  The truth of the matter is […]

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Absolute Value Definition

The concept of absolute value is very important for algebra students to understand. The key thing to know is that absolute value measures distance a number is from zero. If you remember that distance is always a positive number you will be just fine. Key concepts to remember: * the absolute value is the “distance” […]

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Solving One Step Equations (Basic Equations)

College algebra should be so easy- algebra in one simple step!  Not so fast, college math will require a little more work so lets start with the basics of algebra- 1 step equations.  The key to solving any equation is that whatever action you take to one side of an equation you must take the […]

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The Distributive Property

The distributive property is one of the most common areas where algebra students make mistakes.  So to make sure you don’t fail at any distributive property problems lets understand why the distributive property is so important to algebra.  First lets have you understand that the distributive property is just another way to do multiplication problems- […]

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Like Terms (Polynomials)

Like Terms are the basic building block to learning algebra.  Just as sentences have words in algebra we have “terms”.  A term in algebra is nothing more than a combination of a variable and number.  Examples would include 7x,  16y,  43k.  However in algebra we are always looking to collect and combine terms that like […]

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Multiplying And Dividing Positive And Negative Numbers Lesson

One of the top mistakes that cause algebra students to fail is not mastering positive and negative numbers.  The rules are easy however many students tend to confuse and mix the rules up- resulting in poor algebra scores.  Don’t think this problem of mastering the basics in only contained in middle and high school students […]

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Adding And Subtracting Positive And Negative Numbers Lesson

One of the top mistakes that cause algebra students to fail is not mastering positive and negative numbers.  The rules are easy however many students tend to confuse and mix the rules up- resulting in poor algebra scores.  Don’t think this problem of mastering the basics in only contained in middle and high school students […]

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Order of Operations

If I was to list the top factors that cause students problems in math I would place the order of operations right up there at the top of the list!  So if your having problems in math I would almost guarantee that you need to review the order of operations.  Lets quickly go over the […]

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