an absolute value equation is always a twin equation in disguise, so
[tex]6|x-7|=48\implies |x-7|=\cfrac{48}{6}\implies |x-7|=8\implies \pm(x-7)=8 \\\\[-0.35em] ~\dotfill\\\\ +(x-7)=8\implies \boxed{x=15} \\\\[-0.35em] ~\dotfill\\\\ -(x-7)=8\implies x-7=-8\implies \boxed{x=-1}[/tex]
