Answer
This quadrilateral is an isosceles trapezoid.
$x = 3$
Work Step by Step
This quadrilateral is an isosceles trapezoid because it has exactly one pair of parallel sides, and the legs are congruent to one another. We can set the expressions for the legs equal to one another because they are congruent.
$3x + 5 = 5x - 1$
Subtract $5$ from each side of the equation to move constants to the right side of the equation:
$3x = 5x - 6$
Subtract $5x$ from each side of the equation to move variables to the left side of the equation:
$-2x = -6$
Divide both sides of the equation by $-2$ to solve for $x$:
$x = 3$
