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What Does Absolute Value Mean?
Absolute worth defines the distance from zero that a number is on the number line, without considering direction. The absolute worth of a number is never negative. Take a look at some examples.The absolute worth of 5 is 5. The distance from 5 to 0 is 5 devices.
The absolute value of –5 is 5. The distance from –5 to 0 is 5 systems.
The absolute value of 2 + (–7) is 5. When representing the amount on a number line, the resulting point is 5 devices 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 Examples and also EquationsThe many common way 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 means “the absolute value of 6 is 6.”|–6| = 6 indicates “the absolute worth of –6 is 6.”|–2 – x| implies “the absolute worth of the expression –2 minus x.”–|x| implies “the negative of the absolute value of x.”
The number line is not just a method to show distance from zero; it"s additionally a valuable method to graph eattributes and inefeatures that contain expressions through absolute value.
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Consider the equation |x| = 2. To display x on the number line, you have to display every number whose absolute value is 2. There are exactly two areas where that happens: at 2 and at –2:
Now think about |x| > 2. To present x on the number line, you need to show every number whose absolute value is greater than 2. When you graph this on a number line, usage open up dots at –2 and also 2 to suggest that those numbers are not part of the graph:
In general, you get two sets of worths for any type of inehigh quality |x| > k or |x| ≥ k, wright here k is any number.
Now take into consideration |x| ≤ 2. You are looking for numbers whose absolute values 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 all of the oppowebsite numbers in between –2 and 0. When you graph this on a number line, the closed dots at –2 and also 2 suggest that those numbers are had. This is as a result of the inequality using ≤ (less than or equal to) instead of
Math Activities and Lessons Grades 6-8