Chapter 6 - Polygons and Quadrilaterals - 6-3 Proving That a Quadrilateral Is a Parallelogram - Practice and Problem-Solving Exercises - Page 372: 7

$x = 5$

Theorem 6-6 states that in a quadrilateral that is a parallelogram, its diagonals bisect one another. This means that each segment of the bisected diagonal is equal. We can set the two segments of the bisected diagonals equal to one another: $3x = 4x - 5$ $-x = - 5$ Divide both sides by $-1$ to solve for $x$: $x = 5$