Support Course with Tracy Redden

Tracy Redden's support course.

1. A review of graphing lines, finding slope, and finding equations of lines from 2 points and a perpendicular line.

2. Review how to multiply and Factor all types of Polynomials.  I cover Common Factoring, Factor by grouping, Trinomial factoring, and difference and sum of cubes!

3. I show you how to solve all types of linear equations from  basic linear equations to more complicated ones with fractions and variables on both sides.  There are also the ones that end up with no solutions and all reals as a solution.

4. The first step into learning how to solve a quadratic is by factoring.  Here I show you how and explain why.

5. In addition we will look at the domains and restrictions of Rational Expressions.



6. How to Add and Subtract Rational Expressions.  I show you how to find common denominators so you can simplify.



7. How to simplify Complex Fractions.  I show you two different methods.



8. Solving quadratic equations.


... more to come soon.

Solving Linear Equations: Part II

In this section we will solve more complicated linear equations.

Solving Linear Equations YouTube Playlist

If you can, combine same side like terms first then opposite side like terms using the techniques that we have learned in part I. Caution: A common error is to add or subtract a term on the same side of the equal sign.  Only use the opposite operation on opposite sides of the equal sign.

Solve.

Not all equations work out to have a single solution.  Some have infinitely many solutions such as x = x.  Here any number the we chose for x will produce a true statement.  Also, some equations have no solution such as x + 1 = x.

   Contradiction – An equation that will always be false has no solution.
   Identity – An equation that will always be true has any real number, R, as a solution.

It is quite common to encounter linear equations that require us to distribute before combining like terms.

Solve.

Literal equations are difficult for many people because there will be more than one variable.  Just remember that the letters are place holders for some number, so the steps for solving are the same.  Isolate the variable that it asks us to solve for.

Word Problem: The internet connection at the hotel costs $5.00 to log on and $0.20 a minute to access.  If Joe's total bill came to $18.00 then how many minutes did Joe spend on the internet? (Set up an algebraic equation and solve it)

Video Examples on YouTube:

Simplifying Algebraic Expressions

The properties of real numbers are very important in our study of Algebra. These properties can be applied in Algebra because a variable is simply a letter that represents a real number. The distributive property is one that we apply often when simplifying algebraic expressions. Given real numbers a, b, c:

a(b + c) = ab + ac

When multiplying an expression within parentheses you must multiply everything inside by the number or variable that you are distributing.

Introduction to the Distributive Property

Simplify.

When simplifying, we will often have to combine like terms after we distribute.  This step is consistent with the order of operations, multiplication before addition.

Combining Like Terms

Simplify.

Simplifying Algebraic Expressions

To combine like terms, the variable parts have to be exactly the same.  But before combining like terms, generally, we will first distribute if necessary.  When distributing negative numbers notice that the operations change.

Simplify.

Profit Word Problem: Profit is equal to revenues less cost of production.  If the revenue R can be represented by

and the cost C can be represented by

where x represents the number of units produced, find an equation that represents the profit.

Subtracting Variable Expressions: What is the difference between 3x − 4 and −2x + 5?

Video Examples on YouTube:

      

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