Answer
$x = 10$
Work Step by Step
According to theorem 6-18, the diagonals of a rectangle are congruent; therefore, the two diagonals shown are congruent to one another. Let's set the two expressions equal to one another:
$4x - 7 = 2x + 13$
Subtract $2x$ from each side of the equation to move variables to the left side of the equation:
$2x - 7 = 13$
Add $7$ to each side of the equation to move constants to the right side of the equation:
$2x = 20$
Divide both sides by $2$ to solve for $x$:
$x = 10$
