ANSWER
[tex]x=2[/tex]EXPLANATION
From the given triangle;
Side AC and side AC are equal;
[tex]\angle ABC=\angle ACB[/tex]Hence;
[tex]\begin{gathered} AC=AB \\ AB=16x-7 \\ AC=12x+1 \\ 16x-7=12x+1 \end{gathered}[/tex]Add 7 to both sides;
[tex]\begin{gathered} 16x-7=12x+1 \\ 16x-7+7=12x+1+7 \\ 16x=12x+8 \end{gathered}[/tex]Subtract 12x from both sides;
[tex]\begin{gathered} 16x=12x+8 \\ 16x-12x=12x+8-12x \\ 4x=8 \end{gathered}[/tex]Divide both sides by 4;
[tex]\begin{gathered} \frac{4x}{4}=\frac{8}{4} \\ x=2 \end{gathered}[/tex]Therefore, x is 2