Answer
$x = 7.5$
Work Step by Step
According to the triangle-angle-bisector theorem, when a ray bisects the angle of a triangle, the opposite side is divided into two segments that are proportional to the remaining two sides of the triangle.
Let's set up a proportion that compares the segments of the intersected side to the other two sides:
$\frac{15}{14} = \frac{x}{7}$
Use the cross product property to get rid of the fractions:
$14x = 15(7)$
Multiply to simplify:
$14x = 105$
Divide each side of the equation by $14$ to solve for $x$:
$x = 7.5$
