Question

1. solve for x. 10x + 44 8x - 23

Explanation:

Step1: Set up equation

Since the two - non - parallel sides of the trapezoid are equal, we can assume this is an isosceles trapezoid and the mid - segment formula can be used. The length of the mid - segment of a trapezoid is given by $\frac{a + b}{2}$, where $a$ and $b$ are the lengths of the parallel sides. Also, we can set up an equation based on the fact that the non - parallel sides are congruent. Here, we assume that the trapezoid has some property that leads to the equation $10x+44 = 2(8x - 23)$.

Step2: Expand right - hand side

Expand the right - hand side of the equation: $10x+44=16x - 46$.

Step3: Move x terms to one side

Subtract $10x$ from both sides: $44 = 16x-10x - 46$.

Step4: Simplify

Simplify the right - hand side: $44 = 6x-46$.

Step5: Move constant to other side

Add 46 to both sides: $44 + 46=6x$, so $90 = 6x$.

Step6: Solve for x

Divide both sides by 6: $x=\frac{90}{6}=15$.

Answer:

$x = 15$