We are to solve for x
[tex]|x+4|=8[/tex]First, we apply absolute rule
since
[tex]\begin{gathered} |u|=a \\ \text{implies} \\ u=a,u=-a \end{gathered}[/tex]Then the solution to the equation is
[tex]x+4=8,x+4=-8[/tex]Solving the two equations we have
[tex]\begin{gathered} x=8-4 \\ x=4 \end{gathered}[/tex]And
[tex]\begin{gathered} x+4=-8 \\ x=-8-4 \\ x=-12 \end{gathered}[/tex]Therefore, the solutions are '
[tex]x=4,x=-12[/tex]