# Question #e41c3

Oct 11, 2017

Two different numbers can have the same absolute value if one number is the negative of the other. If a number is written in the absolute form, both values must be considered.

#### Explanation:

\The absolute value of a number is the integer or digit by itself, with no signs to indicate if it is positive or negative, or where it lies on a number line, other than the value of the integer.

Example: $7 = + 7 \ne - 7$

In this example, if we have a value of $7$ and if we put a $+$ sign in front of it, we still have a value of $7$, but if we put a $-$ sign in front, we have a different value.

Changing the sign has moved the integer from the positive $7$ position on the number line to the other side of the zero line, all the way back to $- 7$.

In both cases, the absolute value has not changed, it is still $7$.

The absolute value of $7$ is written as $| 7 |$, and:

$| 7 | = 7 \mathmr{and} | - 7 | = 7$

They show the number lines here:
http://www.eduplace.com/math/mathsteps/7/b/