we have the following:
[tex]\begin{gathered} AC=AB+BC \\ \end{gathered}[/tex]replacing:
[tex]\begin{gathered} 38=3x+4+5x-6 \\ 3x+5x=38+6-4 \\ 8x=40 \\ x=\frac{40}{8} \\ x=5 \end{gathered}[/tex]AB:
[tex]3\cdot5+4=15+4=19[/tex]BC:
[tex]\begin{gathered} 5\cdot5-6=25-6=19 \\ \end{gathered}[/tex]therefore,
x = 5
AB = 19
BC = 19
