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01.05 Basic Algebra

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  1. Principles of Algebra – Algebra is a branch of math that uses variables to represent numbers and, when combined with numbers, uses rules or operations to represent statements and equations. Formulas are used in algebra to solve problems.
    1. Algebraic Expressions – Statements with 1 or more terms that are a combination of variables, numbers, and operations.
      1. Expressions are not complete equations, thus don’t have an equal sign, nor do you solve them., you only evaluate and simplify them.
      2. Specific language helps you understand how to think about Algebraic Expressions (e.g. “Ten more than a product of 2 numbers”, or “100 decreased by 2 times a number”)
    2. Evaluating Algebraic Expressions – Process of replacing all variables with numbers, then simplifying to get the value (e.g. 3x + 2y, where x = 5 and y = 2; or 2x/2y, where x = 3 and y = 4)
    3. Simplifying Expressions with Basic Math Operations
      1. Order of Operations is PEMDAS
      2. Properties Attributed to Math Operations are Commutative, Associative, or Distributive
      3. Adding and Subtracting
        1. Same Variable – Monomial (4x + 6x = 10x)
        2. Different Terms – Polynomials 2x(3 – 2y) – x(x + 2y)
      4. Multiplying and Dividing
        1. Monomial by Monomial (2xsquared)(5xy)
        2. Polynomial by Monomial (2xcubed)(3xaquared + 2x – 2)
        3. First, Out, Inner, Last (FOIL) Binomial by Binomial (x + 2) and (x + 3)
        4. Polynomial by Polynomial (x+2)(2x-2) + (4x-2)(x+3)
  2. Solving Equations and Word Problems – Equations are expressions that have an equal sign between them and word problems represent equations
    1. Algebraic Equations – Properties of Equality
    2. Process of Solving Algebraic Equations with 1 variable
    3. Read problems carefully for language of computation
  3. Solving Problems with Formulas
    1. Formula Definition: An equation with a relationship between the variables that is expressed as a rule (I = Prt), and 1 variable is missing.
    2. Solving Problems: Isolate Variables – Move variables, numbers, and expressions in order to find the missing value by Isolating it on one side of equal sign

Reference Links

Video Transcript

Hello and welcome to this quick overview lesson on a basic algebra. Algebra as you may recall is a branch of math that uses variables to represent numbers and, when the two are combined and certain steps are followed these equations can be used to solve a myriad of problems.

So let’s review some terms. A VARIABLE-  A symbol for a number we do not know yet. AN INDEPENDENT variable –  When graphing, the variable on the X-axis

A DEPENDENT variable- When graphing, the  variable on the Y-axis. A CONSTANT is a number on its own. A TERM is a number, variable or both together. And an EXPRESSION is a group of terms.

One of the snags in algebra is knowing how to properly work with negative numbers (whole numbers are also called integers. So when adding or subtracting negative numbers it might be helpful to think of a number line that includes values before and after zero.  When adding negative numbers, you will be moving to or counting to the left on that number line. When subtracting a negative numbers you will move or count to the right.

It’s also tricky in multiplying and dividing negative numbers but they follow a similar rule. When multiplying or dividing different signs the answer is negative and when multiplying and dividing numbers with the same sign the answer is positive.

So let’s look a problem. In this equation we will solve for the variable n. and the answer is n=2….. but how. Let’s first  look together at some steps to follow.

When Solving Linear Algebraic Equations

    1. Remove Parentheses and Combine like terms

    1. Add or Subtract to isolate variable term on one side of the equation

    1. Multiply or Divide  to solve for the variable

If equation contains fractions→multiply  each side of the equation by a common denominator

So let’s put those steps into action. We will remove the parentheses and distribute the negative through. Next we will subtract 4 from each side in order to isolate n. Last we will divide each side by 4 to isolate n further, and we get a final answer of n+2. Of course we can always plug in 2 and see if it is right.

Here are 2 problems for you to practice. Hit pause and solve and rewind if need be. Answers to follow.   

So did you get X = -19/6 and y = 12.48? I hope so!!!

In review, knowing the difference between a variable, a constant, a term and expression will help (especially with word problems.) There are rules to follow when dealing with negative numbers, steps for successfully solving algebraic equations all of which really just requires a little practice! 

Thank you for review some basic algebra here. Now go out and be your best self today and Happy Nursing!