Question

The penny size of a nail indicates the length of the nail. The penny size d
is given by the literal equation d=4n−2
, where n
is the length (in inches) of the nail.

a. Solve the equation for n

n=

b. Use the equation from part (a) to find the lengths of nails with the following penny sizes: 3, 6, and 10.
A 3-penny nail is__inches.

A 6-penny nail is__inches.

A 10-penny nail is__inches.

1. thnahdat
By working with the given linear equation we will see that:
a) n = (d + 2)/4
b)
• A 3-penny nail is_5/4_inches.
• A 6-penny nail is_2_inches.
• A 10-penny nail is_3_inches.

### How to solve the equation for n?

Here we have the linear equation:
d = 4n – 2
We want to solve it for n, it means that we need to isolate n in one side of the equation.
If we first add 2 in both sides of the equation, and then we divide both sides by 4, we will get:
d + 2 = 4n
(d + 2)/4 = n
That is the equation solved for n.
b) The penny size is d, and n is the length of the nail, then:
if d = 3, we have:
n = (3 + 2)/4 = 5/4
if d = 6, then:
n = (6 + 2)/4 = 2
if d = 10, then:
n = (10 + 2)/4 = 3
Thus:
• A 3-penny nail is_5/4_inches.
• A 6-penny nail is_2_inches.
• A 10-penny nail is_3_inches.