You are watching: Is the absolute value of a number always positive
What go Absolute value Mean?
Absolute value defines the distance native zero the a number is ~ above the number line, without considering direction. The absolute worth of a number is never negative. Take it a watch at part examples.The absolute value of 5 is 5. The street from 5 come 0 is 5 units.
The absolute worth of –5 is 5. The distance from –5 come 0 is 5 units.
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 us don"t say that the absolute value of a number is positive. Zero is neither an adverse nor positive.)
Absolute value Examples and also EquationsThe most common method to stand for the absolute value of a number or expression is to surround it v the absolute value symbol: 2 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 value of the expression –2 minus x.”–|x| means “the an unfavorable of the absolute value of x.”
The number heat is not just a method to present distance indigenous zero; it"s also a useful way to graph equalities and also inequalities the contain expressions with absolute value.
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Consider the equation |x| = 2. To present x on the number line, you need to show every number who absolute value is 2. There are exactly two locations where the happens: in ~ 2 and also at –2:
Now think about |x| > 2. To display x ~ above the number line, you require to display every number whose absolute worth is better than 2. As soon as you graph this on a number line, use open dots in ~ –2 and also 2 to show that those numbers space not part of the graph:
In general, you obtain two to adjust of worths for any kind of inequality |x| > k or |x| ≥ k, where k is any number.
Now consider |x| ≤ 2. You are trying to find numbers whose absolute worths are 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 also true for all of the the contrary numbers between –2 and 0. Once you graph this top top a number line, the closeup of the door dots at –2 and also 2 show that those numbers room included. This is due to the inequality making use of ≤ (less 보다 or same to) instead of
Math tasks and Lessons qualities 6-8