The length of a rectangular boat storage shed must be 4 meters more than the width, and the perimeter must be at least 100100 meters. what is the range of values for the width?

I assume it is 100 meters, not 100100 meters.
Length (L)=width(w)+4
Perimeter: 2L+2W>100
Plug L=W+4 into the equation 2L+2W>100:
2(W+4)+2W>100
2W+8+2W>100
4W+8>100
4W>92
W>23
the width needs to be at least 23 meters