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

Question

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## Answers ( No )

(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

(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)