The inequality is:
[tex]5\lvert x-5\rvert-8\le47[/tex]firs we add 8 in bouth sides of the inequation so:
[tex]\begin{gathered} 5\lvert x-5\rvert\le47+8 \\ 5\lvert x-5\rvert\le55 \end{gathered}[/tex]Now we divide by 5 so:
[tex]\begin{gathered} \lvert x-5\rvert\le\frac{55}{5} \\ \lvert x-5\rvert\le11 \end{gathered}[/tex]now we break the absolute value by addig the maximun
[tex]-11\le x-5\le11[/tex]and finally we add 5 so:
[tex]\begin{gathered} -11+5\le x\le11+5 \\ -6\le x\le16 \end{gathered}[/tex]