## Geometry: Common Core (15th Edition)

$x = 4$
According to Theorem 6-15, the diagonals of a rectangle are congruent. Therefore, we can set $LN$ and $MP$, the diagonals of $LMNP$, equal to one another to solve for $x$: $LN = MP$ Substitute with the expressions given for each diagonal: $x = 2x - 4$ Subtract $2x$ from each side of the equation to move variables to the left side of the equation: $-x = -4$ Divide each side by $-1$ to solve for $x$: $x = 4$