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What does Absolute value Mean?
Absolute value describes the distance native zero the a number is ~ above the number line, without considering direction. The absolute value of a number is never negative. Take it a watch at some examples.
The absolute worth of 5 is 5. The street from 5 to 0 is 5 units.
The absolute worth of –5 is 5. The street from –5 to 0 is 5 units.
The absolute value of 2 + (–7) is 5. When representing the amount on a number line, the resulting suggest is 5 units from zero.
The absolute value of 0 is 0. (This is why us don"t say the the absolute value of a number is positive. Zero is neither negative nor positive.)
Absolute worth Examples and Equations
The many common way to represent the absolute worth of a number or expression is to surround it through the absolute worth symbol: 2 vertical straight lines.|6| = 6 means “the absolute value of 6 is 6.”|–6| = 6 means “the absolute worth of –6 is 6.”|–2 – x| means “the absolute worth of the expression –2 minus x.”–|x| means “the an unfavorable of the absolute worth of x.”The number line is not simply a way to display distance native zero; it"s additionally a useful way to graph equalities and inequalities the contain expressions with absolute value.
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Consider the equation |x| = 2. To display x top top the number line, you require to display every number who absolute worth is 2. Over there are precisely two areas where that happens: at 2 and at –2:
Now consider |x| > 2. To present x top top the number line, you require to display every number whose absolute value is higher than 2. Once you graph this top top a number line, use open up dots at –2 and also 2 to indicate that those numbers space not component of the graph:
In general, you gain two set of worths for any type of inequality |x| > k or |x| ≥ k, where k is any type of number.
Now consider |x| ≤ 2. You are searching for numbers whose absolute worths are less than or same to 2. This is true for any number in between 0 and 2, including both 0 and 2. That is likewise true for all of the the contrary numbers between –2 and also 0. When you graph this top top a number line, the close up door dots in ~ –2 and 2 show that those numbers space included. This is due to the inequality using ≤ (less 보다 or equal to) rather of
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