The absolute value, or modulus, of a number is its distance from zero, or essentially its magnitude.
The absolute value produces a positive answer.
We have this definition for the absolute value, taking into account its different values for different signs:
[tex]|x|= \left \{ {{x, \ \ \ x \ \geq \ 0} \atop {-x, \ \ \ x \ \ \textless \ \ 0}} \right.[/tex]
Thus, for [tex]|x+18|=1[/tex], we split the absolute value as such:
[tex]x+18=1[/tex] and [tex]x+18=-1[/tex]
We solve each case.
[tex]x=-17[/tex] and [tex]x=-19[/tex]
We check these solutions.
[tex]|-17+18|=1\\|1|=1\\1=1[/tex]
and
[tex]|-19+18|=1\\|-1|=1\\1=1[/tex]
