Algebra used with the distributive property

QUESTION:

1 = - (-w + 6)
The Distributive Property is an algebra property which is used to multiply a single term and two or more terms inside a set of parentheses. Take a look at the problem below

SOLVE:
1 = - (w + 6)

The minus sign on the outside of the parenthesis means you have to change the sign of everything INSIDE the parenthesis. So, you get this...

1 = w - 6

Because you want the w on one side by itself, you have to get rid of the -6... To make -6 a zero, you have to ADD 6 to it. And what you do to one side of the equal sign, you have to do to the other... So, add 6 to the 1 also. You get this...

7 = w

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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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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.

Math Manipulatives

Math word problems are almost always the type of problems that require an out of the box learning strategy. Some of the most newest on the market manipulative's are great to use such as geoboards to for geometry to CD ROM activity game to walk you through steps of Pre Calculus. And as always you can always use a good pen and paper and write the problem out step by step. These techniques help the student focus visually. Most students qualify under this category of visual learner. This means that the recall and input of information is is pout into a visual concept. When I was in the classroom I always found the one subject that worked best was with manipulative's was math. Even if it didn't seem needed, it always seem to register better in long term memory when i did use them.

Here is a great example of using write it out stratagy.

Question:
Juan has a cell phone that costs $12.95 per month plus $0.25 per minute for each call.
Tiff has a phone that costs $14.95 per month plus $.15 per minute for each call.

For what number of MINUTES do the two plans cost the same?

You can get a feel for this problem by diagramming it out on graph paper. The money is on the left, and the minutes run along the bottom.

Start Juan's diagram at $12.95, and continue slanting it upwards at the rate of $0.25 for each minute.
Start Tiff's diagram at $14.95, and continue slanting it upwards at the rate of $0.15 for each minute.

Where the lines cross is the answer to the problem.

There is an algebraic solution too that I will show you but writing it out would work great if you didnt know the algebraic equation to use.

x = number of minutes

Juan cost = 12.95 + 0.25x

Tiff cost = 14.95 + 0.15x

to cost the same, set the two equations equal to each other

12.95 + 0.25x = 14.95 + 0.15x

combine like terms

0.25x - 0.15x = 14.95 - 12.95

.10x = 2

x = 2/.1

x = 20 minutes