solution set of the inequality

Question

What is the solution set of the inequality (5 + n² ) - n < 50 if the replacement set is {5, 7, 9}.

Answer 1

The inequality (5 + n^2) -n < 50

Solutionset of the inequality replacement set {5,7,9}

Replace n = 5

(5 + 5^2) - 5 < 50

5 + 25 - 5 < 50

25 < 50

Replace n = 7

(5+7^2)-7 < 50

5+49-7 < 50

47 < 50

Replace n = 9

(5+9^2)-9 < 50

5+81-9 < 50

77 > 50

Answer 2

The inequality is (5 + n²) - n < 50 and the replacement set is {5, 7, 9}.

Replace n in (5 + n²) - n < 50 with each value in the replacement set.

n	(5 + n2) - n < 50	True or False?
5	(5 + 52) - 5 < 50 (5 + 25) - 5 < 50 30 - 5 < 50 25 < 50	true
7	(5 + 72) - 7 < 50 (5 + 49) - 7 < 50 54 - 7 < 50 47 < 50	true
9	(5 + 92) - 9 < 50 (5 + 81) - 9 < 50 86 - 9 < 50 77 < 50	false

Since n = 5 and n = 7 makes the inequality true, the solution set of (5 + n²) - n < 50 is {5, 7}.

The solution set is {5, 7}.