absolute value is an important concept in mathematics. The duality of absolute value makes this difficult concept to grasp and difficult for students. But this should not be the case. When considering the absolute value for what it really is, that the distance from a given point to 0 on a number line, we can move this abstraction in perspective. Let us further explore this topic so that it does not present a problem again.
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The absolute value of a number is onlyits distance to 0 on a line number. "| |" Symbol for the absolute value is just used the clip with a number or variables included inside. So | 3 | = 3 because 3 3 units from 0 on the number line. The duality of absolute value comes into play, because the absolute value of both 3 and its additive inverse or -3, which are the same, namely, the third Both 3 and -3 are 3 units from 0 on the line number.
The only thing to remember with absolute value, that if a number is positive then the absoluteThe value is equal to the number given, but if the number is negative, the absolute value of negative or is compared with the number. All this seems too simple. So why the concept of the current problems?
Mastering Mathematics - absolute value
Now, an outcome variable in absolute value of expression and all hell breaks out --- literally. The reason is simple: a variable represents an unknown number. The key word in the preceding sentence is unknown. That is, we do not know if the variable is positive ornegative number. Take the expression | x |. What does that mean the same thing? Well, it all depends. X is positive or negative?
If x is positive, then the expression | X | X is simply equal, but if x is negative, then the expression | x | is equal to x, because the "-" sign in front of x this amount makes it positive. Thinking in mind, two negatives positive. Read the above again, because all the "sticky-ness" comes into play. Most students will say, falsely, that the | x | = xbecause they fail to consider the duality of the absolute value. That is, if we do not know what is the symbol of absolute value, one must consider both cases, that is, if what is inside positive, and if it is negative. If we do this, then the absolute value will never be a problem. To illustrate this, let x = 3. Then | x | = | 3 | = 3 = x, but if x = -3, then | X | = | -3 | = - (-3) = 3 x =-
So do not cringe when you see or hear an absolute value. Remember that all these fundsis the distance to 0 on a number line, and that we must consider both the positives and negatives in dealing with a variable expression. If you do this, you will never reduce these terms. You can then still one more feather in your cap mathematics.
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