Review of Solving Equations

PRINT OUT THIS POST AND MAKE IT THE FIRST PAGE OF YOUR UNIT 2 NOTES!!!

UNIT 2: EQUATIONS

Unit 2 is all about solving linear equations. You've been solving equations for several years, and we expect Algebra students to enter the course with a high degree of proficiency in solving equations with integer coefficients. The first homework assignment in Unit 2 is a chance to knock the rust off your equation-solving skills and get ready for the new material that follows.

Here are our expectations for solving equations algebraically.

Solving

a. Always begin by simplifying the expressions on both sides of the equation completely. Simplifying typically involves getting rid of parentheses by distributing, then adding like terms. After you simplify both sides, you obtain what is called the "simplified equation". This is an important checkpoint. WE MUST SEE THE SIMPLIFIED EQUATION IN YOUR WORK. Some students may be able to get to the simplified equation in one step, others may need more than one step. That doesn't matter. What does matter is that you show the simplified equation. FOR THE TIME BEING STARTING WITH TODAY'S HOMEWORK ASSIGNMENT, YOU MUST DRAW A BOX AROUND THE SIMPLIFIED EQUATION. [See example below.]

b. Once you get to the simplified equation, you begin doing the algebraic inverses to isolate the variable. (By algebraic inverses, we mean adding the same quantity to both sides or multiplying or dividing both sides by the same quantity.) The expectation is that Algebra students do the inverses mentally and do NOT write the inverses on paper.

Checking

a. Do checks in the ORIGINAL equation. You do not need to re-copy the equation, but you must show a straight substitution step where you just replace the variables in the original equation with the solution. In other words, when the reader looks at the first, substitution step of your check, the reader should be able to "see" the original equation.

b. After substituting, you simplify the numerical expressions on both sides of the equation. If there are grouping symbols, you must show the simplified value of the expression inside the grouping symbols. [See example below.]

c. We do not require a check on every equation. We will tell you when to check.

Solution Set

a. Whether or not you are required to do a check, always finish your work with a "therefore" statement (3-dot triangle), followed by the solution in braces.

b. If your solution did not check and you could not find your error, write "Does not check" in place of the solution set. Never write a solution set if you can't get your solution to check!

Study the examples below carefully and follow them when doing assignment 2A.

Mrs. Skinner's Algebra Students

Be sure  to have your Unit 1 Quiz A in class tomorrow in your Test/Quiz section of your binder.

Algebra Adage - Hints!

A few hints for the Algebra Adage Homework!!
    Remember if its a fraction it should stay in fraction from until you have simplified the numerator and denominator to single values that can then be divide.

F:   1 - (-2) +3|4 - (5+6) +7|  --> Treat absolute value signs as parentheses -- complete operations inside the inner most parentheses first!!  
    1 - (-2) + 3|4 - 11 +7|
    1 - (-2) + 3|-7+7|
    1 - (-2) + 3|0|
     1 + 2 + 0
        3 + 0
           0

M: |-1| - (-2)-3(-4)-(-5)(-6)-(-7)  --> Identify what has to be multiplied and what is being added
    |-1| - (-2)-3(-4)-(-5)(-6)-(-7)  --> The blue values are being multiplied!!  You can also think of what is green as -1 times the number.
     1+2 +12 - 30 +7  --> Be sure to add from left to right start with the first two terms and them go from there.  Don't combine terms in the middle.

Hope these hints help!!  Enjoy your weekend!
     

Practice: Set Notation and Set Operations Answer Key (Classwork)

1a. Rule: {all real numbers between -1 and 3 inclusively}
     Set-Builder: {x: -1 < x < 3}
     Interval: [-1, 3]

1b. Rule: { all real numbers greater than 2}
      Set-Builder: { x: x > 2}
      Interval: (2, infinity)

1c. Rule {all real numbers between -2 and 0 exclusively}
     Set-Builder: {x : -2 < x < 0}
     Interval: (-2, 0)

1d.  Rule {all real numbers less than or equal to 1}
       Set-Builder: {x : x < 1}
       Interval: ( negative infinity, 1]

3b.  A' = {-1, 1, 3, 5}
       B' = {-1, 0, 1, 3, 4, 5}
    A U B = {-2, 0, 2, 4}
    A n B = {-2, 2}

3c.  B is a sub set of A since all the elements in set B are in set A.

4b. S' is all Iroquois Middle School Students who are not in Student Council
      S n E is all of the 8th graders that are in Student Council

5a. A'             5b.  (A U B)'             5c. (A n B)'           5d.   A n B n C        
5e. A n B      5f.  (A n C) U (B n C)

6a. R          6b.   { } --> null set or empty set        6c. I      6d.  N

Hope this helps!!

Set Operations

In class on Monday, you will receive a packet entitled "Set Notation and Set Operations". Here is a site with a video and notes that review the operation of complementation (finding the complement of a set):

http://www.crctlessons.com/complement-of-a-set.html

Note that this site uses the "prime" (apostrophe) notation to indicate the complement of a set, e.g., A' means "the complement of set A". There are other notations for the complement of a set, as shown in the packet. You should be familiar with all of these notations. Also, note the definition and notation for null set and empty set, which are synonyms referring to the set that contains no elements.

This video reviews the set operations of intersection and union:

http://www.youtube.com/watch?v=Hek8Y3FlAm0

Note the use of interval notation. :-)

After you've completed the practice exercises in the packet, check your answers below (sorry for the small print).

Please bring your questions to class tomorrow and be ready to practice set operations.

Mr. R