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What Does Absolute Value Mean?
Absolute value explains the distance from zero that a number is on the number line, without considering direction. The absolute worth 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 units.
The absolute worth of –5 is 5. The distance from –5 to 0 is 5 devices.
The absolute worth of 2 + (–7) is 5. When representing the sum on a number line, the resulting point 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 Value Instances and also EquationsThe most prevalent way to recurrent the absolute value of a number or expression is to surround it with the absolute value symbol: 2 vertical straight lines.|6| = 6 means “the absolute worth of 6 is 6.”|–6| = 6 indicates “the absolute value of –6 is 6.”|–2 – x| means “the absolute worth of the expression –2 minus x.”–|x| suggests “the negative of the absolute value of x.”
The number line is not simply a way to present distance from zero; it"s likewise a valuable means to graph echaracteristics and inequalities that contain expressions via absolute worth.
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Consider the equation |x| = 2. To show x on the number line, you have to show eincredibly number whose absolute worth is 2. Tbelow are precisely 2 areas where that happens: at 2 and also at –2:
Now take into consideration |x| > 2. To show x on the number line, you have to present eincredibly number whose absolute value is greater than 2. When you graph this on a number line, usage open up dots at –2 and 2 to indicate that those numbers are not part of the graph:
In general, you obtain 2 sets of values for any type of inehigh quality |x| > k or |x| ≥ k, wright here k is any type of number.
Now think about |x| ≤ 2. You are trying to find numbers whose absolute values are much less than or equal to 2. This is true for any type of number in between 0 and also 2, including both 0 and also 2. It is additionally true for all of the opposite numbers in between –2 and 0. When you graph this on a number line, the closed dots at –2 and 2 show that those numbers are included. This is as a result of the inequality using ≤ (less than or equal to) rather of
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