Absolute Value in Algebra

This symbol--> |x| represents the absolute value of x, which is the number without its sign. |+3| = 3. |−3| = 3.

Geometrically, |x| is the distance of x from 0.

Both 3 and −3 are a distance of 3 units from 0. |3| = |−3| = 3. Distance, in mathematics, is never negative.


The absolute value leaves a positive unchanged, and makes a negative positive
An absolute value is written like this: |x|, and is read as "the absolute value of x." Note: In certain places, such as calculator and computer programs, you may see it written as abs(x), which naturally means "the absolute value of x," but |x| is the accepted way to write it on your homework and tests.

To force a number to be negative, you can write -|x|. This takes the number, makes it positive, and then negates it. Remember -- just putting a negative sign in front of a number doesn't make it negative. If the number was already negative then you just made it positive! Using the absolute value guarantees we have a positive value so that the negative sign will definitely make it negative.



EXAMPLE:

Rewrite this expression without using absolute value notation:

1) |x+1|+4|x+3| given that x<-3

If x < –3 then x+ 1< 0 and x+ 3 <0. In general, when a<0 |a| = –a, thus

|x+1|+ 4|x+3| =

–(x+1) – 4(x +3) provided x < –3 or simplifying ...

–x – 1 – 4x – 12 =

–5x – 13 when x < –3

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Ordering fraction from least to greatest

How do i put fractions in order from least to greatest?

Change the denominators to be common and then convert.
EX. 4/5,5/15, 6/30
Put these in order
you have to see what is the LCM for each of the denominators. Like 30. so 4/5 turns into 24/30. I used 30 as my common denominator and to get the numerator I said how many times does 5 go into 30? 6 times! So 6 times 4 equals 24 which is my new numerator. Do this with all the fractions and then you can just put them in order by the top number.

Mean Median and Mode Range and Outliers

RANGE DEFINITION:
The difference between the highest and the lowest numbers in a set of numbers.
HOW TO FIND THE RANGE:
Subtract the lowest number from the biggest and you get the range!
FIND THE RANGE
ex. 3,6,3,7,9
9-3=6 6 IS THE RANGE


MEAN DEFINITION:
average of all the numbers
HOW TO FIND THE MEAN
found by dividing the sum of the numbers by the amount of numbers added.
FIND THE MEAN
ex. 3,6,3,7,9
3+6+3+7+9=28
28 divided by 5=5.6 5.6 is your mean

MEDIAN DEFINITION:
The number directly in the middle
HOW TO FIND THE MEDIAN:
List all numbers in order from least to greatest.
You count over to the middle. If there are two numbers in the middle, add them and divide by two.
FIND THE MEDIAN
EX. 3,6,3,7,9
3,3,6,7,9 The middle number is 6. 6 is your median.
MODE DEFINITION:
The mode is the number that you see more than any other number.
The number or numbers that occur most often in a set of numbers.
EX. 3,6,3,7,9
the number that occurs the most is 3. 3 is your mode.

DEFINITION OF OUTLIER:
In statistics, an outlieR is an observation that is numerically distant from the rest of the data. Basically the number that seems to be way off from the other numbers.

EX: 3,6,5,85
The outlier would be 85

Learning Integers & Non Integers

What is an integer? { ... -3, -2, -1, 0, 1, 2, 3, ... }
Integers are the whole numbers, negative whole numbers, and zero. For example, 43434235, 28, 2, 0, -28, and -3030 are integers, but numbers like 1/2, 4.00032, 2.5, Pi, and -9.90 are not. We can say that an integer is in the set: {...3,-2,-1,0,1,2,3,...} (the three dots mean you keep going in both directions.)

It is often useful to think of the integers as points along a 'number line', like this:

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10_____________________________________________________


Note that zero is neither positive nor negative.


About integers
The terms even and odd only apply to integers; 2.5 is neither even nor odd. Zero, on the other hand, is even since it is 2 times some integer: it's 2 times 0. To check whether a number is odd, see whether it's one more than some even number: 7 is odd since it's one more than 6, which is even.

Another way to say this is that zero is even since it can be written in the form 2*n, where n is an integer. Odd numbers can be written in the form 2*n + 1. Again, this lets us talk about whether negative numbers are even and odd: -9 is odd since it's one more than -10, which is even.

Every positive integer can be factored into the product of prime numbers, and there's only one way to do it for every number. For instance, 280 = 2x2x2x5x7, and there's only one way to factor 280 into prime numbers.

There are also things called non integers....such as fractions,Pi, and repeating decimals.


Example Question:
y is a integer.
-3 < y < 2
what are all the possible values of y?

Answer:
So it would be all the numbers in between -3 and +2
Answer: -2,-1,0,+1

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Substituting equations to solve.

Example Question:
x= y-7
-y=2x=8


Example to solve substituting equations to solve..

substitute 1st equation into the 2nd one

-y = 2*(y-7) - 8
-y = 2y - 14 - 8
-y = 2y - 22
-y - 2y = -22
-3y = -22
y= 22/3

substitute the value of y in the 1st equation to get x.

About Private Tutoring Math...

My name is Diana and I am currently a certified Florida teacher. I own my own tutoring company and come across many students with math homework questions with nowhere to turn for help. I am creating this blog to provide math homework help and new and up to date useful learning strategies and information to help students achieve correct math answers with up to date information on the latest math help manipulative's, new online teaching and learning strategies and information on teaching skills for both teachers and students. I will be covering all topics in math including Algebra, Geometry, Calculus, and Pre Calculus. Also, I will cover all the math equations and simple word problems with addition, multiplication, division,and subtraction. I am trying to reach all ages with math homework help. I have strategies and manipulative suggestions that will help you take math homework questions and soar into new heights with a brightened understanding.

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