document.write( "Question 647364: Hi, I'm in a hybrid math class at my college, so i don't get to see my teacher for another week and i have no idea how to do this problem. Can you please help me?
\n" ); document.write( " I don't understand the \"K\" rule:
\n" ); document.write( " K={K if K>(or equal to)0
\n" ); document.write( " {-K if K< 0
\n" ); document.write( "I have an example from my book here: (I am just having a hard time with this because my book does not explain anything.)
\n" ); document.write( " absol. (x-2)^2 absol.
\n" ); document.write( "I thought you would do this: (x-2)(x-2) and multiply: x^2+4
\n" ); document.write( "The answer in the book says (x-2)^2 is the answer along with: absol.K absol.=K if K> (or equal to) 0
\n" ); document.write( "I dont understand how to find out what K rule to use if there is no real number value.\r
\n" ); document.write( "\n" ); document.write( "Thank you,
\n" ); document.write( "Sydney \n" ); document.write( "
Algebra.Com's Answer #406156 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Absolute value bars either make negatives into positives or keep positives\r\n" );
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document.write( "Rule for getting rid of the absolute value bars | | around a number:\r\n" );
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document.write( "1. If the number inside the | | is positive, simply erase the | |.\r\n" );
document.write( "2. If the number inside the | | is negative, change the number to \r\n" );
document.write( "   positive and erase the absolute value bars.\r\n" );
document.write( "3. The absolute value of zero is zero, |0| = 0\r\n" );
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document.write( "Examples:\r\n" );
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document.write( " |3| = 3 because 3 is already positive so you just erase the | |.\r\n" );
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document.write( "|-3| = 3 because -3 is negative and so you change the sign to positive\r\n" );
document.write( "       and erase the | |.\r\n" );
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document.write( "|57| = 57 because 57 is already positive and you just erase the | |\r\n" );
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document.write( "|-234| = 234 because -234 is negative and so you change the sign to positive\r\n" );
document.write( "       and erase the | |.\r\n" );
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document.write( "That's all there is to the rule.\r\n" );
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document.write( "The rule your teacher gave you amounts to the same thing.  Here is why:\r\n" );
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document.write( "First part:\r\n" );
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document.write( "|K|= K if K>(or equal to)0\r\n" );
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document.write( "\"If K is greater than or equal 0\" is the same as saying \r\n" );
document.write( "\"K is positive or zero\", and so you just erase the absolute value \r\n" );
document.write( "bars around K\r\n" );
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document.write( "The second part is what seems different but isn't.  It's confusing because \r\n" );
document.write( "often a positive letter stands for a negative number. That's what K is \r\n" );
document.write( "in this part of the rule. K is a positive letter standing for a negative\r\n" );
document.write( "number.\r\n" );
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document.write( "|K| = -K if K < 0\r\n" );
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document.write( "That says if POSITIVE K stands for a NEGATIVE number (less than 0), then\r\n" );
document.write( "to make it positive you will need to put another negative sign before that\r\n" );
document.write( "negative number that K stands for already has so that the negative sign that \r\n" );
document.write( "K already has will multiply by the negative sign that you put in front of\r\n" );
document.write( "whatever negative number K stands for and that negative sign will cause the\r\n" );
document.write( "result to be a positive number.\r\n" );
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document.write( "I agree that's very confusing!  So just remember that the absolute value bars\r\n" );
document.write( "just say \"If it's positive, leave it positive, and if it's negative,\r\n" );
document.write( "make it positive\".\r\n" );
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document.write( "-------------------------------\r\n" );
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document.write( "Let's look at some examples with letters:\r\n" );
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document.write( "Ex: Simplify |x-3| if possible\r\n" );
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document.write( "No absolute values are ever negative. You cannot remove the absolute value \r\n" );
document.write( "bars because -- since you cannot know what x is, you cannot tell whether x-3\r\n" );
document.write( "is positive or negative.  For instance if x were 1, x-3 would be -2, a\r\n" );
document.write( "negative number.  So you cannot remove the absolute value bars. \r\n" );
document.write( "So it is not possible to simplify |x-3|. You cannot remove the bars.\r\n" );
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document.write( "Ex: Simplify |3y+12| if possible.\r\n" );
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document.write( "You can simplify by taking out a positive 3\r\n" );
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document.write( "       3|y+4|\r\n" );
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document.write( "but you have to leave the absolute value bars because if y were equal\r\n" );
document.write( "to, say, -9, then y+4 would be negative.  So you couldn't simplify it \r\n" );
document.write( "further.\r\n" );
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document.write( "Now let's look at the example in your book:\r\n" );
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document.write( "Simplify |(x-2)²| if possible.\r\n" );
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document.write( "Notice that (x-2) is SQUARED.  When you square a POSITIVE number you\r\n" );
document.write( "get a POSITIVE number.  But also when you SQUARE a NEGATIVE number you\r\n" );
document.write( "ALSO get a POSITIVE number!   Therefore in the case of (x-2)² you\r\n" );
document.write( "will NEVER get a negative number, regardless of what x is. That's because\r\n" );
document.write( "even if (x-2) is negative, it will then get squared and the answer will be positive.  Therefore you can simplify by removing the absolute value bars\r\n" );
document.write( "because (x-2)² will be positive regardless of whether (x-2) is positive or negative.\r\n" );
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document.write( "That's why the absolute value bars are not necessary around something\r\n" );
document.write( "SQUARED.\r\n" );
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document.write( "That's why |(x-2)²| can be simplified by removing the absolute values,\r\n" );
document.write( "getting just (x-2)² without absolute value bars.\r\n" );
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document.write( "To recap:\r\n" );
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document.write( "You cannot remove that absolute values for |x-2| because what's inside might\r\n" );
document.write( "be negative.  However you CAN remove the absolute value bars for |(x-2)²|\r\n" );
document.write( "because what's inside cannot be negative.\r\n" );
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document.write( "I hope this clears it up a little for you.  Don't worry about the \"K\".  Just\r\n" );
document.write( "think of absolute value bars as \"positive makers or keepers\".\r\n" );
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document.write( "Edwin

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