Question

what is the absolute value of 2x+1 greater than or equal to -1 ?

Answer 1

first of all this is not possible. The absolute value can not equal a negative number but:

same or opposite
Same opposite
2x+1>=-1 -(2x+1)>=-1
2x>=0 2x+1<=1
x>=0 2x<=0
x>=0 or x<=0
which is all real numbers but there is no solution to this problem!

Answer 2

thank you! is it no solution or all reals?

Answer 3

actually I mis stated it, since it is greater than or equal to, all real numbers are greater than -1. If it was only =, we would get 0 but that would not be a valid solution.
so all real numbers