Using the law of sines, we have
[tex]\dfrac{\sin B}{2x-24}=\dfrac{\sin C}{x-2}[/tex]
but angles B and C are congruent, so the sine terms cancel and we're left with
[tex]\dfrac1{2x-24}=\dfrac1{x-2}\implies2x-24=x-2\implies x=22[/tex]
