3 In this question you must show detailed reasoning.
A gardener is planning the design for a rectangular flower bed. The requirements are:
- the length of the flower bed is to be 3 m longer than the width,
- the length of the flower bed must be at least 14.5 m ,
- the area of the flower bed must be less than \(180 \mathrm {~m} ^ { 2 }\).
The width of the flower bed is \(x \mathrm {~m}\).
By writing down and solving appropriate inequalities in \(x\), determine the set of possible values for the width of the flower bed.