Answer:
The simplify form of the provided equation in form of n is
. For penny size 3, 6, and 10. the lengths of nail is 5/4, 2 and 3 respectively.
Step-by-step explanation:
Consider the provided equation.

Where n is the length (in inches) of the nail and d is the penny size.
Part(a) Solve the equation for n.
Consider the provided equation and add 2 to the both sides.


Now divide both the sides by 4.


The simplify form of the provided equation in form of n is
.
Part (B) To find the lengths of nails with the following penny sizes: 3, 6, and 10.
For penny size 3.
Substitute d=3 in
.


For penny size 6.
Substitute d=6 in
.



For penny size 10.
Substitute d=10 in
.



Hence, for penny size 3, 6, and 10. the lengths of nail is 5/4, 2 and 3 respectively.