Answer
$x = 6$
Work Step by Step
$T$ marks the point of concurrency of a triangle's angle bisectors. Therefore, $T$ is the center of the circle that is inscribed inside the triangle, so any point on that circle is equidistant from $T$.
In this diagram, $U$ and $V$ are located on the inscribed circle; therefore, $TU$ is equal to $TV$. We can now set these distances equal to one another to solve for $x$:
$3x - 12 = 5x - 24$
Subtract $3x$ from each side of the equation to isolate the variable on one side of the equation:
$-12 = 2x - 24$
Add $24$ to each side of the equation to isolate constants on one side of the equation:
$2x = 12$
Divide each side of the equation by $2$ to solve for $x$:
$x = 6$
