You are watching: The distance of a number from zero on a number line

## What walk Absolute worth Mean?

Absolute value defines the **distance from zero** the a number is on the number line,** **without considering direction. The absolute value of a number is never ever negative. Take a look at some examples.

The absolute worth of –5 is 5. The street from –5 to 0 is 5 units.

The absolute worth of 2 + (–7) is 5. Once representing the sum on a number line, the resulting point is 5 devices from zero.

The absolute value of 0 is 0. (This is why we **don"t** say the the absolute worth of a number is positive. Zero is neither an unfavorable nor positive.)

## Absolute worth Examples and Equations

The most common method to stand for the absolute worth of a number or expression is come surround it through the absolute worth symbol: 2 vertical directly lines.|6| = 6*means “*the absolute value 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 line is not just a way to present distance from zero; it"s also a useful means to graph equalities and also inequalities that contain expressions with absolute value.

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Consider the equation |*x*| = 2. To display *x* ~ above the number line, you require to present every number who absolute worth is 2. There are exactly two areas where that happens: at 2 and at –2:

Now take into consideration |*x*| > 2. To show *x* ~ above the number line, you require to display every number who absolute worth is better than 2. Once you graph this on a number line, use open up dots at –2 and also 2 to indicate that those numbers room not component of the graph:

**In general, you obtain two to adjust of worths for any inequality | x| > k or |x| ≥ k, where k is any number.**

Now think about |*x*| ≤ 2. Friend are searching for numbers whose absolute values are less than or equal to 2. This is true for any kind of number in between 0 and also 2, consisting of both 0 and 2. That is additionally true for every one of the the contrary numbers between –2 and 0. Once you graph this ~ above a number line, the close up door dots in ~ –2 and 2 suggest that those numbers are included. This is due to the inequality utilizing ≤ (less than *or same to*) instead of

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