[tex]\begin{gathered} \text{Given} \\ |x-5|-2=10 \end{gathered}[/tex][tex]\begin{gathered} |x-5|-2=10 \\ \\ \text{Add 2 to both sides} \\ |x-5|-2+2=10+2 \\ |x-5|\cancel{-2+2}=12 \\ |x-5|=12 \\ \\ \text{Apply absolute value rule where} \\ \text{If }|u|=a,a>0,\text{ then }u=a\text{ or }u=-a \\ u=x-5,a=12 \\ \\ x-5=-12\text{ or }x-5=12 \\ \\ x-5=-12 \\ x=-12+5 \\ x=-7 \\ \\ x-5=12 \\ x=12+5 \\ x=17 \\ \\ \text{Therefore, the solution is} \\ x=-7\text{ or }x=17 \end{gathered}[/tex]
