In the diagram, the radius of the outer circle is
2x cm and the radius of the inside circle is 6 cm.
the area of the shaded region is 1607 cm?
what is the value of x?

assuming we are looking for the area of a flat donut where the smaller circle is the hole and the larger circle includes the space made by the hole all the way out to the donut's edge:

if you want to post the diagram, i can confirm by imaginations and assumptions.

step-by-step explanation:

im assuming we are tying to find the area that is in the larger circle also not contained in the small circle. maybe it kind of looks like a flat donut that we are trying to find the area of.

if the larger circle has radius 2x, then the area is .

if the smaller circle has radius 6, then the area is .

again we are trying to find that is outside the smallee circle but inside that larger. so we need to subtracr the areas above to find the area of this flat donut:

.

we are aslo told this area is 1607.

this means we have the following should be true:

we want to solve first for .

add on both sides:

divide both sides by :

square root both sides: