# Chapter 6 - Polygons and Quadrilaterals - Chapter Review - Page 423: 37

$x = 2$

#### Work Step by Step

According to the trapezoid midsegment theorem, in a quadrilateral that is a trapezoid, the midsegment is parallel to the bases and is half the sum of the base lengths. Let's set up the equation for the midsegment of the trapezoid to find the value of $x$: $5x - 3 = \frac{1}{2}[(6x - 1) + (3)]$ Evaluate parentheses first: $5x - 3 = \frac{1}{2}(6x + 2)$ Divide both sides by $\frac{1}{2}$ to get rid of the fraction. Dividing by a fraction means to multiply by its reciprocal: $10x - 6 = 6x + 2$ Subtract $6x$ from each side of the equation to move variables to the left side of the equation: $4x - 6 = 2$ Add $6$ to each side of the equation to move constants to the right of the equation: $4x = 8$ Divide both sides by $4$ to solve for $x$: $x = 2$

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