You are watching: The distance a number is from zero
What does Absolute worth Mean?
Absolute value defines the distance native zero the a number is on the number line, without considering direction. The absolute value of a number is never ever negative. Take a watch at part examples.
The absolute worth of 5 is 5. The distance from 5 to 0 is 5 units. 
The absolute value of –5 is 5. The distance from –5 to 0 is 5 units.
The absolute worth of 2 + (–7) is 5. When representing the sum on a number line, the resulting suggest is 5 devices from zero.
The absolute worth of 0 is 0. (This is why we don"t say that the absolute worth of a number is positive. Zero is neither an unfavorable nor positive.)
Absolute value Examples and also Equations
The many common method to represent the absolute worth of a number or expression is come surround it v the absolute worth symbol: 2 vertical right lines.|6| = 6 means “the absolute worth of 6 is 6.”|–6| = 6 means “the absolute value of –6 is 6.”|–2 – x| means “the absolute value of the expression –2 minus x.”–|x| means “the an adverse of the absolute value of x.”The number heat is not simply a means to display distance from zero; it"s additionally a useful method to graph equalities and inequalities the contain expressions v absolute value.
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Consider the equation |x| = 2. To display x top top the number line, you require to present every number whose absolute value is 2. Over there are exactly two places where the happens: in ~ 2 and also at –2:
Now consider |x| > 2. To show x ~ above the number line, you require to present every number who absolute worth is higher than 2. As soon as you graph this on a number line, use open up dots at –2 and 2 to suggest that those numbers are not part of the graph:
In general, you get two to adjust of values for any type of inequality |x| > k or |x| ≥ k, whereby k is any number.
Now take into consideration |x| ≤ 2. Friend are looking for numbers whose absolute values are less than or same to 2. This is true for any kind of number in between 0 and 2, consisting of both 0 and also 2. That is additionally true for all of the opposite numbers in between –2 and also 0. When you graph this top top a number line, the closeup of the door dots in ~ –2 and also 2 suggest that those numbers space included. This is because of the inequality utilizing ≤ (less 보다 or same to) instead of
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