By moving -4 to the right hand side, we get
[tex]\begin{gathered} |12-3x|=11+4 \\ |12-3x|=15 \end{gathered}[/tex]Now, by the properties of the absolute values, this last equation becomes in 2 conditions:
[tex]\begin{gathered} a)\text{ 12-3x=15} \\ b)12-3x=-15 \end{gathered}[/tex]From condition a), by moving 12 to the right hand side, we get
[tex]\begin{gathered} -3x=15-12 \\ -3x=3 \end{gathered}[/tex]and x is given by
[tex]\begin{gathered} x=\frac{3}{-3} \\ x=-1 \end{gathered}[/tex]Now, from condition b), by moving 12 to the right hand side, we have
[tex]\begin{gathered} -3x=-15-12 \\ -3x=-27 \end{gathered}[/tex]then, x is given by
[tex]\begin{gathered} x=\frac{-27}{-3} \\ x=9 \end{gathered}[/tex]Therefore, the answer is the union of both solution, that is, the answer is the third option: x=-1, 9
