Answer :
[tex]|8w+2| + 2=0 \ \ \ subtract\ 2 \ to\ both\ sides \\\\|8w+2| =-2 \\\\absolute \ value \ can \ not \ be \ negative, \ is \ equal \ to \ zero \ or \ greater \ than \ zero[/tex]
[tex]|8w+2|+2=0\\\\
|8w+2|=-2\\\\Formula\ for\ absolute\ value\\\\
|a|=a,\ for\ a \geq 0\\ or\\|a|=-a,\ for\ a<0\\\\\
1.\\8w+2 \geq 0\\\\
8w \geq -2\\\\
w \geq -\frac{1}{4}\\\\
8w+2=-2\\\\
8w=-4\\\\w=-\frac{1}{2}\\\\2.\\8w+2 <0\\\\8w<-2\\\\w<-\frac{1}{4}\\\\8w+2=2\\\\8w=0\\\\ w=0\\\\ Summing\ all\ conditions:\\\\ No\ solutions.[/tex]
