Question

isosceles trapezoid jklm has legs JK and LM and base KL if JK=8x-9, kl=7x+10 and LM=10x+2 find the value of x

Answer 1

The domain:
$8x-9 > 0\to 8x > 9\to x > \dfrac{9}{8}\\\\7x+10 > 0\to 7x > -10\to x > -\dfrac{10}{7}\\\\10x+2 > 0\to 10x > -2\to x > -0.2\\\\D:x\in\left(\dfrac{9}{8};\ \infty\right)$

If the trapezoid JKLM is an isosceles trapezoid then the legs are congruent.
$|JK|=|LM|\to 8x-9=10x+2\ \ \ |+9\\\\8x=10x+11\ \ \ |-10x\\\\-2x=11\ \ \ |:(-2)\\\\x=-5.5\notin D$

Answer: Such a trapezoid does not exist.