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What does Absolute value Mean?
Absolute value describes the distance from zero the a number is top top the number line, without considering direction. The absolute value of a number is never negative. Take a watch at part examples.The absolute value of 5 is 5. The street from 5 to 0 is 5 units.
The absolute worth of –5 is 5. The distance from –5 come 0 is 5 units.
The absolute value of 2 + (–7) is 5. Once representing the amount on a number line, the resulting allude is 5 units from zero.
The absolute worth of 0 is 0. (This is why we don"t say that the absolute value of a number is positive. Zero is neither negative nor positive.)
Absolute worth Examples and also EquationsThe many common way to stand for the absolute value of a number or expression is come surround it through the absolute worth symbol: two vertical straight lines.|6| = 6 means “the absolute worth 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 negative of the absolute worth of x.”
The number line is not just a means to display distance indigenous zero; it"s likewise a useful method to graph equalities and inequalities the contain expressions with absolute value.
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Consider the equation |x| = 2. To show x top top the number line, you require to show every number whose absolute value is 2. Over there are precisely two places where the happens: in ~ 2 and also at –2:
Now take into consideration |x| > 2. To display x top top the number line, you need to display every number whose absolute value is greater than 2. When you graph this top top a number line, use open up dots at –2 and 2 to show that those numbers space not component of the graph:
In general, you acquire two set of values for any type of inequality |x| > k or |x| ≥ k, wherein k is any type of number.
Now consider |x| ≤ 2. Friend are trying to find numbers whose absolute worths are much less than or equal to 2. This is true for any type of number between 0 and also 2, including both 0 and also 2. It is likewise true for every one of the the contrary numbers between –2 and also 0. As soon as you graph this ~ above a number line, the closeup of the door dots in ~ –2 and 2 show that those numbers room included. This is as result of the inequality using ≤ (less 보다 or same to) instead of
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