Question

A neighborhood of -4 with a radius 2 is described by what?
less than or equal to is this: <=
A. lx+4l <= 2
B. lx-4l<2
C. lx-2l<4
D. lxl<2
E. lx+4l<2

Answer 1

open neighborhood last one

Answer 2

can you give a more in depth explanation please?

Answer 3

sure. saying that
\[|x-b|<p\] is the same as
\[-p<x-b<p\] i.e.
\[b-p<x<b+p\] which is another way of saying that x is within p units of b, either to the right or to the left

Answer 4

for example
\[|x+4|<2\] means x is less that 2 units from -4

Answer 5

we can solve for x to get
\[-2<x+4<2\] or
\[-6<x<-2\] in interval notation
\[(-6,-2)\] an interval centered at -4 and extending 2 units to the right and left

Answer 6

thanks!