Richard+Mallory+Absolute+Value

Richard Mallory Absolute Value

Media Files That Will Blow Your Mind The media file that is below shows all the stages of how to solve absolut value problems this has helped me before when I have needed help on a problem http://www.youtube.com/watch?v=qRFX_HK-6Ik Non Media this link that is below helped me in showing me how to figure out the problem then had some examples at the bottom that i could work out and then it would show how to solve that problem. http://www.themathpage.com/Alg/absolute-value.htm Copyright © 2001-2008 Lawrence Spector Questions or comments? E-mail: themathpage@nyc.rr.com

The concept of absolute value has many uses, but you probably won't see anything interesting for a few more classes yet. For now, you can view absolute value as the distance from zero. (There is a technical [|definition] for absolute value, but you probably won't see this for quite a while, if ever.) Look at the number line:

The absolute value of  //x//  , denoted "|   //x//   |" (and which is read as "the absolute value of   //x//   "), is regarded as the distance of   //x//   from zero. This is why absolute value is never negative; absolute value only asks "how far?", not "in which direction?". This means that  | 3 | = 3  , because   3   is three units to the right of zero, and also   | –3 | = 3   , because   –3   is three units to the left of zero.

(Warning: The absolute-value notation is //bars//, not parentheses or brackets. Use the proper notation, as the other notations do //not// mean the same thing.) It is important to note that the absolute value bars do NOT work in the same way as do parentheses. Whereas  –(–3) = +3  , this is NOT how it works for absolute value: Given  –| –3 |  , first handle the absolute value part, taking the positive and converting the absolute value bars to parentheses: –| –3 | = –(+3)   Now you can take the negative through the parentheses: –| –3 | = –(3) = **–3**   So you see that if you take the negative of an absolute value, you will get a negative number for your answer.
 * ** Simplify   –| –3 |   .  **

When typing, such as in e-mail, the "pipe" is usually used to indicate absolute value. The "pipe" is probably a shift-key somewhere north of the "Enter" key on your keyboard. While the "pipe" denoted on the physical keyboard key may look "broken", the typed character should display on your screen as a solid vertical bar. If you cannot locate a "pipe" character, you can use "  abs   " instead, so that "the absolute value of negative   3   " would be typed as "   abs(–3)   ".

Here are some more sample simplifications: | –8 | = ** 8 ** Copyright © Elizabeth Stapel 2006-2008 All Rights Reserved | 0 – 6 | = | –6 | = **6**   | 5 – 2 | = | 3 | = **3**    | 2 – 5 | = | –3 | = **3**    | 0(–4) | = | 0 | = **0**    Why is the absolute value of zero equal to "   0   "? Ask yourself: how far is zero from  0   ? Zero units, right? So  | 0 | = 0. | 2 + 3(–4) | = | 2 – 12 | = | –10 | = **10**   –| –4| = –(4) = **–4**    –| (–2)2 | = –| 4 | = **–4**    –| –2 |2 = –(2)2 = –(4) = **–4**    (–| –2 |)2 = (–(2))2 = (–2)2 = **4**    Sometimes you will be asked to insert an inequality sign between two absolute values, such as: Whereas  –4 > –7   (it is further to the right than is   –7   ), we are dealing here with the absolute values. Since: | –4 | = 4   | –7 | = 7,    ...and   4 < 7  , then the solution is: | –4 | **__<__** | –7 |.
 * ** Simplify   | –8 |   .  **
 * ** Simplify   | 0 – 6 |   .  **
 * ** Simplify   | 5 – 2 |   .  **
 * ** Simplify   | 2 – 5 |   .  **
 * ** Simplify   | 0(–4) |   .  **
 * ** Simplify   | 2 + 3(–4) |   .  **
 * ** Simplify   –| –4 |   .  **
 * ** Simplify   –| (–2)2 |   .  **
 * ** Simplify   –| –2 |2  **
 * ** Simplify   (–| –2 |)2   .  **
 * ** Insert the correct inequality:   | –4 | _ | –7 |  **

Then the number inside the absolute value (the "argument" of the absolute value) was positive anyway, we didn't change the sign when we took the absolute value. But if the argument was negative, we did change the sign; namely, we changed the "understood" "plus" into a "minus". This leads to one fiddly point which may not come up in your homework now, but will probably show up on tests later: When you are dealing with [|variables] , you cannot tell the sign of the number or the value that is contained in the variable. For instance, given the variable  //x//  , you cannot tell by looking whether there is, say, a "   2   " or a "   –4   " contained inside. So if I ask you for the absolute value of  //x//  , what would you do? Since you cannot tell, just by looking at the letter, whether or not the variable contains a positive or negative value, you would have to consider these different cases. If  //x// > 0   (that is, if   //x//   is positive), then the value won't change when you take the absolute value. For instance, if  //x// = 2  , then you have   | //x// | = | 2 | = 2 = //x//. In fact, for //any// positive (or zero) value of  //x//  , the sign would be unchanged, so: For  //x//   __>__   0, | //x// | = //x// On the other hand, if  //x// < 0   (that is, if   //x//   is negative), then it will change its sign when you take the absolute value. For instance, if  //x// = –4  , then   | //x// | = | –4 | = + 4 = –(–4) = –//x//. In fact, for //any// negative value of  //x//  , the sign would have to be changed, so: For  //x// < 0, | //x// | = –//x// This is a case in which the "minus" sign on the variable does not indicate "a number to the left of zero", but "a change of the sign from whatever the sign originally was". This "–" does not mean "the number is negative" but instead means that "I've changed the sign on the original value". http://www.purplemath.com/modules/absolute.htm

Stapel, Elizabeth. "Absolute Value." __Purplemath__. Available from __http://www.purplemath.com/modules/absolute.htm__. Accessed 11 November 2008 Problems |-1|=


 * 1 + - 2|=


 * 2+ 1| + | -5 |=

-|-8|=


 * 3-4-5|=

Definitions and Theorem For every nenzero real number a. the absolute value of a, denoted |a|, is the positive number of the pair a and the opposite of a. for example, |-3| is the positive number of the pair -3 and 3, so |-3|=3. similatiry, |7|=7 and |-8|=8. the absolute value of 0, denoted |0|, is defined to be 0. Formally, we make the definition Also called [|numerical value.] the magnitude of a quantity, irrespective of sign; the distance of a quantity from zero. The absolute value of a number is symbolized by two vertical lines, as |3| or |−3| is equal to 3. The numerical value of a real number without regard to its sign. For example, the absolute value of -4 (written |-4|) is 4. Also called //numerical value//. The value of a number without regard to its sign. For example, the absolute value of +3 (written |+3|) and the absolute value of -3 (written |-3|) are both 3.

[Date] [Month] 2008

Example Problems

example |x-6|= 9 when you have an absolute value always chnage the sign to + and then solve it out  (x-6)=9 or -(x-6)=9 x-6=9 or x-6=-9 x=15 or x=3

example 2 1+3=4 (because every thing the basolute is positive)
 * 1-3|= 4

example 3 -|8+9|= -17 you add them together and then you distibute the negative (order of Operations) -(8+9)=-17 distribute the negative -8-9=-17

Answers to the Problems 1. = 1 this is the answer because -1 is one place away from zero 2. = 1 here the answer is 1 because we have to do what is inside the brackets first and then find the absolute value 3. = 8 here 8 is the answer because 2 1 and 5 are all and when they are added together their sum is 8 4. = -8 the ansewer is -8 because even though it is 8 away from 0 we have to distribute the negetive sign 5. = 6 here the answer is 6 because we must first add together what is inside the brackets and then we can find the absolute value which is 6 because it is 6 away from 0