[tex]-1=-|5x+7|\\\\Formula\ for\ absolute\ value\\\\
|a|=a,\ for\ a \geq 0\\ or\\|a|=-a,\ for\ a<0\\\\\\
-1=-(5x+7)\ \ \ \ or\ \ \ \ -1=-(-5x-7)\\
-1=-5x-7\ \ \ \ or\ \ \ \ -1=5x+7\\
6=-5x\ \ \ \ or\ \ \ \ -8=5x\\
\boxed{x=-\frac{6}{5}\ \ \ or\ \ \ x=-\frac{8}{5}}[/tex]
