Answer
$x = 1$
Work Step by Step
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:
$3x + 1 = 8x - 4$
Subtract $8x$ from each side of the equation to move variables to the left side of the equation:
$-5x + 1 = -4$
Subtract $1$ from each side of the equation to move constants to the right side of the equation:
$-5x = -5$
Divide each side by $-5$ to solve for $x$:
$x = 1$
