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What Does Absolute Value Mean?
Absolute worth explains the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never before negative. Take a look at some examples.The absolute value of 5 is 5. The distance from 5 to 0 is 5 devices.
The absolute worth of –5 is 5. The distance from –5 to 0 is 5 systems.
The absolute value of 2 + (–7) is 5. When representing the sum on a number line, the resulting allude is 5 systems from zero.
The absolute value of 0 is 0. (This is why we don"t say that the absolute worth of a number is positive. Zero is neither negative nor positive.)
Absolute Value Instances and EquationsThe a lot of widespread method to recurrent the absolute value of a number or expression is to surround it via the absolute value symbol: 2 vertical right lines.|6| = 6 indicates “the absolute worth of 6 is 6.”|–6| = 6 means “the absolute value of –6 is 6.”|–2 – x| indicates “the absolute value of the expression –2 minus x.”–|x| implies “the negative of the absolute worth of x.”
The number line is not just a way to show distance from zero; it"s additionally a valuable way to graph echaracteristics and inefeatures that contain expressions via absolute value.
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Consider the equation |x| = 2. To show x on the number line, you have to display eextremely number whose absolute worth is 2. Tbelow are exactly two places wright here that happens: at 2 and also at –2:
Now think about |x| > 2. To display x on the number line, you should display eexceptionally number whose absolute worth is higher than 2. When you graph this on a number line, usage open dots at –2 and also 2 to show that those numbers are not component of the graph:
In basic, you acquire two sets of worths for any kind of inehigh quality |x| > k or |x| ≥ k, wbelow k is any kind of number.
Now take into consideration |x| ≤ 2. You 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 2, including both 0 and 2. It is also true for all of the opposite numbers in between –2 and also 0. When you graph this on a number line, the closed dots at –2 and 2 suggest that those numbers are contained. This is as a result of the inetop quality making use of ≤ (much less than or equal to) instead of
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