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i need help plz help and here is a explanation i hope this helped
step-by-step :
Formally, the absolute value of a number is the distance between the number and the origin. This is a much more powerful definition than the "makes a negative number positive" idea. It connects the notion of absolute value to the absolute value of a complex number and the magnitude of a vector.
The absolute value of x, denoted "| x |" (and which is read as "the absolute value of x"), is 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 not only that | 3 | = 3, because 3 is three units to the right of zero, but also that | –3 | = 3, because –3 is three units to the left of zero. You can see this on the following number line:
abs(-3) = abs(3) = 3
Warning: The absolute-value notation is bars, not parentheses or brackets. Use the proper notation; 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:
Simplify –| –3 |.
Given –| –3 |, I first need to handle the absolute-value part, taking the positive of the insides (the "argument of" the absolute value) and then converting the absolute value bars to parentheses:
–| –3 | = –(+3)
Now I can take the negative through the parentheses:
–| –3 | = –(3) = –3
As this illustrates, if you take the negative of an absolute value (that is, if you have a "minus" sign in front of the absolute-value bars), you will get a negative number for your answer.
Side note: When typing math as text, such as in an e-mail, the "pipe" character is usually used to indicate absolute values. 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 like a "broken" line, the typed character should display on your screen as a solid vertical bar. If you cannot locate a "pipe" character, you can use the "abs()" notation instead, so that "the absolute value of negative 3" would be typed as "abs(–3)".
Here are some more example simplifications:
Simplify | –8 |.
| –8 | = 8
Simplify | 0 – 6 |.
| 0 – 6 | = | –6 | = 6
Simplify | 5 – 2 |.
| 5 – 2 | = | 3 | = 3
Simplify | 2 – 5 |.
| 2 – 5 | = | –3 | = 3
Simplify | 0(–4) |.
| 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.
Simplify | 2 + 3(–4) |.
| 2 + 3(–4) | = | 2 – 12 | = | –10 | = 10
Simplify –| –4 |.
–| –4| = –(4) = –4
In the next three examples, pay particular attention to the difference that the location of the square makes, with respect to the "minus" signs.
Simplify –| (–2)2 |.
–| (–2)2 | = –| 4 | = –4
Simplify –| –2 |2
–| –2 |2 = –(2)2 = –(4) = –4
Simplify (–| –2 |)2.
(–| –2 |)2 = (–(2))2 = (–2)2 = 4
