Question

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

Answer 1

(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

Answer 2

(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)