To solve for x, we first need to convert all fractions to a common denominator.

14 9/16 - x = 6 3/4 + 1 2/5

Convert 9/16 to a fraction with denominator 4:
14 9/16 - x = 6 3/4 + 1 10/20

Now, convert 3/4 to a fraction with denominator 20 and 2/5 to a fraction with denominator 20:
14 9/16 - x = 6 15/20 + 1 8/20

Now, perform the addition:
14 9/16 - x = 7 23/20

Now simplify and convert the mixed numbers to improper fractions:
14 + 9/16 - x = 7 + 23/20
(224 + 9)/16 - x = (140 + 23)/20
233/16 - x = 163/20

Now, find a common denominator and subtract:
(2335)/(165) - x = 163/20
1165/80 - x = 163/20

Now, solve for x by isolating it on one side of the equation:
1165/80 - 163/20 = x
(116520 - 16380) / 80 = x
(23300 - 13040) / 80 = x
10260 / 80 = x
128.25 = x

Therefore, x = 128.25.