start by dividing both sided by -5
[tex]\frac{-5}{-5}|3+4k|=-\frac{115}{-5}[/tex][tex]|3+4k|=23[/tex]when we have an absolute we obtain two equations, one for the positive value and one for the negative value
[tex]\begin{gathered} 3+4k=23 \\ -(3+4k)=23 \end{gathered}[/tex]solve each of them
[tex]\begin{gathered} 3+4k=23 \\ 4k=23-3 \\ 4k=20 \\ k=\frac{20}{4}=5 \end{gathered}[/tex]for the second equation
[tex]\begin{gathered} -(3+4k)=23 \\ -3-4k=23 \\ -4k=23+3 \\ -4k=26 \\ k=-\frac{26}{4}=-6.5 \end{gathered}[/tex]the solutions for k are -6.5 and 5
