## Geometry: Common Core (15th Edition)

$EF = 9$
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. We are asked to find $EF$, which is the midsegment of this trapezoid. Let's set up the equation to find the length of the midsegment: $2x + 1 = \frac{1}{2}[(15) + (x - 1)]$ Evaluate parentheses first: $2x + 1 = \frac{1}{2}(x + 14)$ Divide both sides by $\frac{1}{2}$ to get rid of the fraction. Dividing by a fraction means to multiply by its reciprocal: $2(2x + 1) = x + 14$ Distribute on the left side of the equation: $4x + 2 = x + 14$ Subtract $x$ from each side of the equation to move variables to the left side of the equation: $3x + 2 = 14$ Subtract $2$ from each side of the equation to move constants to the right side of the equation: $3x = 12$ Divide both sides by $3$ to solve for $x$: $x = 4$ Now we plug $2$ in for $x$: $EF = 2(4) + 1$ Multiply first, according to order of operations: $EF = 8 + 1$ Add to solve: $EF = 9$