# Absolute value

A positive number can be designated by a numeral preceded by a plus sign or by a numeral without a sign. Every real number is either positive or negative. The two numerals +7 and -7 have different signs but the numerical part of each is 7.

This part of the numeral designates the absolute value of the number. The absolute value of a is denoted by | a | (a vertical bar on each side of the quantity).

**Example**

If we designate the absolute value of an algebraic expression such as

$$\mid x+1 \mid$$

and x has a value such that x+1 is a negative number, then the absolute value of the expression will be negative of the expression . If x+1<0,

$$\mid -7 \mid =7$$

$$\mid 7 \mid =7$$

**Video lesson**

Simplify $$-|7|+4+|-3|$$