Question

(b) the figure is a trapezoid with the top base labeled (6x + 1), the bottom base labeled (x), and a midline (or median) labeled (4x - 2). the legs of the trapezoid are marked as equal (isosceles trapezoid).

Explanation:

Step1: Apply trapezoid midsegment theorem

The midsegment of a trapezoid is equal to the average of the two bases, so:
$$4x-2=\frac{(6x+1)+x}{2}$$

Step2: Simplify right-hand side

Combine like terms in the numerator:
$$4x-2=\frac{7x+1}{2}$$

Step3: Eliminate the denominator

Multiply both sides by 2:
$$2(4x-2)=7x+1$$
$$8x-4=7x+1$$

Step4: Solve for x

Subtract $7x$ from both sides, then add 4 to both sides:
$$8x-7x=1+4$$
$$x=5$$

Answer:

$x=5$