Just had my first lecture today and was working on some practice problems, but got stuck on this one. All I have been introduced to so far is the equation of a sphere, but I don't really know what else to do with this.
I completed the square on both sides of the inequality by adding 1/4 to each side and made the middle of the inequality a sphere centered at (0,0,1/2).
Here is my full attempt. The inequality represents the region on/between the spheres centered at (0,0,1/2) with radii 1 1/4 and 3 1/4. The region contains all of the points on the sphere with radius 1 1/4 and includes all of the points of the second sphere except the outermost points where r = 3 1/4.
I think this might be right, but I just thought I'd check with you guys.