For what natural values of n is the difference (2-2n) - (5n-27) positive?

(2 - 2n) - (5n - 27) > 0

-7n + 27 + 2 > 0

-7n > - 29

n < 29/7 < 4.143

So the natural values of n to make the expression positive are

1, 2, 3 and 4 (answer)

(2-2n) - (5n-27) >0

distribute

2-2n - 5n + 27 >0

combine like terms

-7n + 29 >0

subtract 29 from each side

-7n> - 29

divide by - 7 (flips the inequality)

n < - 29/-7

n <4.14

natural numbers are 1,2,3,4 ...

n must be 1,2,3,4

Answer: 1,2,3,4