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# Lesson 6.1: Absolute Value

## Symbol

$|\phantom{\rule{.3em}{0ex}}\text{vertical bar}$

## Explanation

Vertical bars for absolute value

Vertical bars are used in a mathematical expression which displays the absolute value of a quantity. The absolute value of a numeral is its distance from zero, in either direction, on the number line. It is an undirected value, the value without a positive or negative sign. The braille configuration of both the opening and closing vertical bars is dots one two five six.

Vertical bars used for absolute value are considered to be a sign of grouping, so it should be treated as a mathematical symbol and spaced similarly to parentheses. A numeric indicator is not needed for a number immediately following a regular vertical bar.

### Example 1

$|5|=5$
⠳⠢⠳⠀⠨⠅⠀⠼⠢

### Example 2

$|-5|=5$
⠳⠤⠢⠳⠀⠨⠅⠀⠼⠢

### Example 3

$|-7.5|=7.5$
⠳⠤⠶⠨⠢⠳⠀⠨⠅⠀⠼⠶⠨⠢

### Example 4

$|2-6|=|-4|=4$
⠳⠆⠤⠖⠳⠀⠨⠅⠀⠳⠤⠲⠳⠀⠨⠅⠀⠼⠲

### Example 5

absolute value nested inside absolute value

$||-2|+|3||=|5|=5$
⠳⠳⠤⠆⠳⠬⠳⠒⠳⠳⠀⠨⠅⠀⠳⠢⠳⠀⠨⠅⠀⠼⠢

### Example 6

$|x|$
⠳⠭⠳

### Example 7

$|-\frac{2}{3}|$
⠳⠤⠹⠆⠌⠒⠼⠳

### Example 8

$-|-5|=-5$
⠤⠳⠤⠢⠳⠀⠨⠅⠀⠤⠼⠢

### Example 9

$\text{What is the value of}\phantom{\rule{.3em}{0ex}}|-9|\text{?}$
⠠⠺⠓⠁⠞⠀⠊⠎⠀⠞⠓⠑⠀⠧⠁⠇⠥⠑⠀⠕⠋⠀⠸⠩⠀⠳⠤⠔⠳⠀⠸⠱⠦

### Example 10

$4○|-6|$
⠼⠲⠀⠫⠉⠀⠳⠤⠖⠳