Danielle, Inequalities

here's a link to practice absolute value equations and inequalities

http://www.blogger.com/post-create.g?blogID=2979614811124141785

When One Side of Inequality is Divided by a Value

Ex.
6a + 3 < -3
   -4
First multiply both sides by -4

6a + 3(-4) < -3(-4)
6a + 3 > 12

Now subtract 3 from both sides to isolate the coefficient 
6a - 3 > 12 -3
6a > 9

Now divide 6 from both sides to isolate the variable
6a > 9
6      6
a > 2/3

graph!


--(--------------------->
 2/3

Harrison siad...

In class on friday I wasn't sure what the symbals for union and intersection were and what they ment. JoJo explained that a U sign ment union which means the lines on your graph don't ever cross because they go in opposite directions. Than he explained that intersection was an n symble. If A={a, b, c, d} And B={a, c, e, f} than the union of the two would be {a, b, c, d, e, f}
the intersect would be {a, c}

A2A (2011): Tyler, September 10

A2A (2011): Tyler, September 10: "On Friday we talked about and took notes on additive inverse, set notation, and distributive property (JoJo's favorite property). Then, as a..."

Geometrical

Geometrical is the distance of a value from zero.

B.O.B. Chapter 3

There is a BIG difference between learning and just being there. Learning is an interactive sport; not a spectator sport. There has to be a conversation between us, back and forth, as we work through the material. Learning doesn't happen when I talk and you listen; learning happens when you have a conversation -- with me and with each other.

I am going to offer you up to 5 bonus points on your test with completion of a simple assignment.  I would like you to post your reflections on the material covered so far.  Just comment on this post.  To get that bonus on your test, the kind of post I'd like you to make should have one or more of these characteristics:

• A reflection on a particular class (like the first paragraph above-how did that class enhance your learning?).
• A reflective comment on your progress in the course.
• A comment on something that you've learned that you thought was "cool".
• A comment about something that you found very hard to understand but now you get it! Describe what sparked that "moment of clarity" and what it felt like.
• Have you come across something we discussed in class out there in the "real world" or another class? Describe the connection you made.

Absolute Value Symbol

|x|

Absolute value is the distance from zero.

Example:

|-3|=3

|3|=3

Amelia

Chapter 3 Test Monday November 1st

CHAPTER 3 TEST MONDAY NOV. 1ST

3.1  - 3.3

Tutorial design team to be named soon!

Scribe Post

Scribe Post for October 22 2010

In class today we talked more about how to solve compound inequalities with AND or OR. This is review from chapter 3 section 2.

Solving With And

1st treat both sides of the inequality like its own problem, so solve for both sides.
X+1<> 3
X <> 5
2nd Because the inequalities are joined by AND the solution will include all numbers between 8 and 5.

On a graph the problem would look like this: ___(___________)___
5 8

This shows that your answer is all numbers between 5 and 8.

Solving With OR

1st solve both sides of the problem individually.
6X – 4 < 2X or -3x < -9
-4 < -4X or X < 1
1>X or X > 3

2nd since the solution set are joined with OR the solution will include all the numbers either one of the two inequalities in step 1

Here’s how the problem looks in graph form: X>3 or X<1 color="#cc0000">+++++)+(+++++++++>
1 3
Because X can be all numbers less than one it can also be written as: (-∞, 1)
Because X can be all numbers greater than three it can also be written as: (3, ∞ )


Note: ( ) = < >
[ ] = ≤ ≥

4X ≤ 12
X ≤ 4
This can also be written as: (-∞, 4]

Ok, good stuff Next scribe will be Cole.

Website for help and explinations x

Dr. Math.com is a helpful website to go to if you need more help outside of class on a certain type of problem

http://mathforum.org/library/drmath/drmath.high.html

Danielle, Interval Notation - Here is an easier way of understanding intervals

Interval Notation:  (description) (diagram) Open Interval:   (a, b)  is interpreted as a < x < b  where the endpoints are NOT included.(While this notation resembles an ordered pair, in this context it refers to the interval upon which you are working.) (1, 5) Closed Interval:  [a, b]  is interpreted as a < x < b  where the endpoints are included. [1, 5] Half-Open Interval:  (a, b]  is interpreted as a < x < b where a is not included, but b is included. (1, 5] Half-Open Interval:  [a, b) is interpreted as a < x < bwhere a is included, but b is not included. [1, 5) Non-ending Interval:   is interpreted as x > a where ais not included and infinity is always expressed as being "open" (not included). Non-ending Interval:   is interpreted as x < b whereb is included and again, infinity is always expressed as being "open" (not included).

Sribe Post For October 21 2010

In class today we just did homework that was suppose to be done yesterday night, so i am just going to redo a couple of different hw problems that we did in class today.
Chapter 3 section 1

9. 4x + 1 ≥ 21 - solve and give answer in both interval and graph forms
First step: clear fractions- there are no fractions
Second step: simplify each side separately- both sides are already simplified
Third step: isolate the variable terms on one side. 4x + 1 ≤ 21
4x ≤ 20
Fourth step:isolate the variable- 4x ≥ 20
4x/4 ≥ 20/4
x ≥ 5
The answer in graph form: <-|-|-|-|-|-|-|-|-|-|-[-|-|-|-|-> and in interval form: [5, ∞)
-5 0 9
Now that we know have to solve the inequalities lets move a bit faster.
22. m-2(m-4) ≤ 3m
m-2m-8≤3m
-m-8≤ 3m
-m-8 + -m ≤ 3m + -m
8 ≤ 2m
4 ≤ m
Lets now try a different type of problem form the hw.
Solve the linear equation
31. 5(x+3)-2(x-4)=2(x+7)

Simplifying

5(x + 3) + -2(x + -4) = 2(x + 7)

Reorder the terms:

5(3 + x) + -2(x + -4) = 2(x + 7)

(3 * 5 + x * 5) + -2(x + -4) = 2(x + 7)

(15 + 5x) + -2(x + -4) = 2(x + 7)

Reorder the terms:

15 + 5x + -2(-4 + x) = 2(x + 7)

15 + 5x + (-4 * -2 + x * -2) = 2(x + 7)

15 + 5x + (8 + -2x) = 2(x + 7)

Reorder the terms:

15 + 8 + 5x + -2x = 2(x + 7)

Combine like terms: 15 + 8 = 23

23 + 5x + -2x = 2(x + 7)

Combine like terms: 5x + -2x = 3x

23 + 3x = 2(x + 7)

Reorder the terms:

23 + 3x = 2(7 + x)

23 + 3x = (7 * 2 + x * 2)

23 + 3x = (14 + 2x)

Solving

23 + 3x = 14 + 2x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2x' to each side of the equation.

23 + 3x + -2x = 14 + 2x + -2x

Combine like terms: 3x + -2x = 1x

23 + 1x = 14 + 2x + -2x

Combine like terms: 2x + -2x = 0

23 + 1x = 14 + 0

23 + 1x = 14

Add '-23' to each side of the equation.

23 + -23 + 1x = 14 + -23

Combine like terms: 23 + -23 = 0

0 + 1x = 14 + -23

1x = 14 + -23

Combine like terms: 14 + -23 = -9

1x = -9

Divide each side by '1'.

x = -9

Simplifying

x = -9

<-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|->

-10 0 7

Ok lets try something a bit different again.

Solve each inequality, giving its solution set in both interval and graph forms.

37.-4 <>6

First step: add 5 on both sides of the inequality

-4 + 5 < x < 11

Second step: simplify- 1

<-|-|-|-|-|-|-[-|-|-|-|-|-|-|-|-|-]-|-|>

-5 9 13 0 9 13

Even if my wonderful scribe post did not help you maybe this guy with a power point can. =)

http://www.youtube.com/watch?v=MJ4dCBmYwvU

Just copy paste the "ULR" into your browser address bar

For the next scribe i choice Harrison

Section 3.1, Ifeayani

Today in class we went over solving compound inequalities with “and” or “or”.

inequality- A statement between two expressions indicating which one has greater value.

solving a compound inequality with “and”


ex1: x+19 and x-23

step1: solve each inequality in the compound inequality individually.
x+19 and x-23
x8 x5


step2:Since the inequalities are joined with and, the solution set of the compound inequality will include all numbers that satisfy both inequalities in step 1 (the intersection of the solution sets).
[-----------]
|-|-|-|-|-|-|-|-|-|-|-|-
0 2

ex2: 2x+1 7 and 3x-4 17
(subtract 1) 2x 6 3x 21
(divide by 2) x 3 and x 7

set notation: [3,7]


solving a compound inequality with or

you solve step 1 the same way but your answer has to include everything that satisfies either equation.

ex1 with “or” would be all real numbers


ex2 with “or” would also be all real numbers

The next scribe post will be William

Things To Remember!

Useful Facts to remember while doing a compound inequality:

1. You read left to right while doing an inequality

Please add on!

If you are a visual learner, a Venn diagram is useful to show you how to find the intersection of the two sets of numbers.

For example:

Example 1: Solve for 3 x + 2 < style="font-style: italic; ">x – 5 > –11

Solve each inequality separately. Since the joining word is “and,” this indicates that the overlap or intersection is the desired result.

x < style="font-style: italic; ">x > –3 indicates all the numbers to the right of –3. The intersection of these two graphs is all the numbers between –3 and 4. The solution set is

Another way this solution set could be expressed is

On the Venn diagram, You would put All numbers more than -3 in the first circle( at the left), all number in between -3 and four in the middle circle, and all numbers greater than 4 in the right circle!

When a compound inequality is written without the expressed word “and” or “or,” it is understood to automatically be the word “and.” Reading { x | − 3 < x < style="font-style: italic; ">x” position, you say (reading to the left), “ x is greater than –3 and (reading to the right) x is less than 4.” The graph of the solution set is shown in Figure 1 .

Figure 1 x is greater than –3 and less than 4.

Read more: http://www.cliffsnotes.com/study_guide/Compound-Inequalities.topicArticleId-38949,articleId-38862.html#ixzz12xCBh5zM

Taken from:http://www.cliffsnotes.com/study_guide/Compound-Inequalities.topicArticleId-38949,articleId-38862.html

Chapter Three More Symbols

When dwriting your answer on a number line it is important to know a couple of symbols.
A circle that is filled in means that the number is included in the solution.
A circle that is not filled in and just the outline of a circle means that the number is not included in the solution.
Amelia

Symbols in Chapter 3

Here are some more symbols used in chapter three.
< is less than
> is greater than
< with a line underneith it is less than or equal to
> with a line underneith it is greater than or equal to
Sorry I couldnt figure out how to put the line under the sign.
Amelia

Danielle Scribe Post Chapter 3 Section 3.1

Today in class we went over 2 test problems that no one got right and we also went over some of section 3.1.
2 Test Problems
#11. John has 20 ounces of a 20% of salt solution, How much salt should he add to make it a 25% solution?

concentration= 20%=.20
amount= 20 ounces =20
added= x

Equation for solving problem #11 :
(.20)20 + 1x = .25(20+x)
4 + x = 5 + .25 x
.75x = 1
x= 1/.75
x=4/3 oz.

#12. A tank has a capacity of 10 gallons. When it is full, it contains 15% alcohol. How many gallons must be replaced by an 80% alcohol solution to give 10 gallons of 70% solution?

Equation for solving #12 :
1.5 -. 15x + .80x  = 7
After solving this equation you should get
x=8.46 gallons

Next we went over some of Section 3.1, mainly interval notation
and set notation

example of interval notation
x  > -1

example of set notation
( -1, infinity symbol)

We did a problem in class to help us distinguish interval notation from set notation

4x-5 > 13
      +5        +5
4x/4 > 18/4 

x> 9/2
interval notaion

[9/2 , infinity symbol]
set notation    

the next scribe :Ifeanyi

New Symbols Used in Chapter 3

Here are some new symbols that are used throughout chapter 3. We haven't covered all of them yet, but hopefully when we start learning about them you will already know what they mean because of this post!

∞=Infinity

-∞=Negative Infinity

(-∞,∞)=The set of real numbers

∪=Set Union

∩=Set Intersection

How to Figure out Commission?

On the most recent test we had, there was a problem on figuring out interest, but first you had to find out how much commission was. I didnt know what commission was, so heres the definition.
commission- a sum or percentage allowed to agents, sales representatives , etc.
commission salary- the money you are paid when you sell a service or product for a company

Emma, 3.1 Linear Inequalities in One Variable

Today we talked about Inequalities.
An Inequality is whether (or not) the left side equals the right side.
Inequality Symbols:
> less than
< greater than
≤ less than or equal to
≥ greater than or equal to
≠ not equal to 
≈ approximately equal to
You CAN NOT include ∞ (infinity) because it never ends.


As an example, JoJo showed that Hana's height (5'3") is less than Christine's height (5'7")
Hana's height < Christine's height
But if Hana's height ≤ Christine's height
Hana could be 5'6" if the inequality were true


Solve for x:
4x - 5 ≥ 13
Add 5 to both sides
4x + 0 ≥ 18
4x ≥ 18
Divide 4 from both sides
4x/4 ≥ 18/4
x ≥ 9/2  Interval notation
•-----|----|----|--> Number line
9/2  5    6    7
[9/2, ∞)
^        ^ not included 
included                       } Set notation
Don't forget to CHECK!


4(5) - 5 ≥ 13
20 - 5 ≥ 13
15 ≥ 13 Yes, the inequality is true.


We don't have any homework over the break. 
The next scribe will be Danielle.

Scribe Post

Today in class we decided to move the test to tomorrow and went over problems that were hard for us on the last couple homework assignments. Since we get an extra night to study my post is going to be going over important things to know for the test. I am going to go over some problems and terms that are important to know from section 2.1-2.3. I am not going to go over everything from these sections because some things have been explained in other scribe posts. I am just going to go over things I have found confusing from these sections. Also remember that you can bring in a page of math tweets to use during your test tomorrow. They have to be printed from the favorite page or a screen shot of the favorite page then printed. If you dont do this you can't use them during the test.

Section 2.1
Recognizing Conditional Equations, Identities, and Contradictions
1.Conditional
One solution
Final line is x=a number
2. Contradiction
None; solution set is 0 with a / threw it
Final line is false, such as -15=120
3. Identity
Infinite; solution set, all real numbers
Final line is true, such as 0=0

Section 2.2
Solving for a Specified Variable
Example: Solve for t.
prt=I
(pr)t=I associative property
(pr)t/pr=I/pr divide by pr.
t=I/pr
Steps for solving for a Specified Variable
Step 1: Transform so that all terms contain the specified variable are on one side of the equation and all terms without that variable are on the other side.
Step 2: If necessary, use the distributive property to combine the terms with the specified variable. The result should be the product of a sum or the difference and the variable.
Step 3: Divide each side y the factor that is the coefficient of the specified variable.
Section 2.3
It's important to remember how to translate words to mathmatical expressions.
*This was explained on Christines scribe post earlier this week.
Remember the Difference Between Expression and Equation
Expression:
Example: x=5
Equation:
Example: x+2=4
Solving an Investment Problem
Example:
After winning the state lottery, Mark LeBeau has $40,00 to invest. He will put part of the money in an account paying 4% interest and the remainder into stocks paying 6% interest. His accountant tells him that the total annual income from these investments should be $2,040. How much should he invest at each rate?
Step 1: Reas the problem again. We must find the two amounts.
Step 2: Assign a variable
Let x= the amount to invest at 4%
Let 40,000-x= the amount to invest at 6%
The formula for interest is I=prt. Here the time, t, is one year. Make a table to organize the given information.
You can look up the table for this equation on page 82 in your math book.
Step 3: Write an equation. We do so without clearing decimals.
.04+.06(40,000-x)=2040
Step 4: Solve the equation. We do so without clearing decimals.
.04+.06(40,000)-.06x=204o Distributive Property
.04x+2,400-.06x=20 Multiply
-.02x+2,400=2,040 Combine Like Terms
-.02x=-360 Subtract 2,400
x=18,00 Divide by -.02
Step 5: State the answer. Mark should invest $18,000 at 4%. At 6%, he should invest $40,000-$18,000=$22,000.
Step 6: Check bby finding the annual interest at each rate; they should total $2,040.
.04($18,000)=$720 and .06($22,000)=$1,320
$720+$1,320=$2,040, as required.
The Next Scribe Post will be done by Emma

Who founded algebra

I was wondering who founded algebra. So i looked it up and I found that a man named Al-Khwarizmi is considered to to be the father of algebra.  

BoB -Blogging on Blogging Chapter 2

There is a BIG difference between learning and just being there. Learning is an interactive sport; not a spectator sport. There has to be a conversation between us, back and forth, as we work through the material. Learning doesn't happen when I talk and you listen; learning happens when you have a conversation -- with me and with each other.

I am going to offer you up to 5 bonus points on your test with completion of a simple assignment.  I would like you to post your reflections on the material covered so far.  Just comment on this post.  To get that bonus on your test, the kind of post I'd like you to make should have one or more of these characteristics:

• A reflection on a particular class (like the first paragraph above-how did that class enhance your learning?).
• A reflective comment on your progress in the course.
• A comment on something that you've learned that you thought was "cool".
• A comment about something that you found very hard to understand but now you get it! Describe what sparked that "moment of clarity" and what it felt like.
• Have you come across something we discussed in class out there in the "real world" or another class? Describe the connection you made.