Question

Determine which integer makes the inequality 6(n − 5) < 3(n + 4) true.

S:{11}
S:{14}
S:{30}
S:{42}

Answer 1

6(n − 5) < 3(n + 4)

6n - 30 < 3n + 12 // Distribute the 6 and 3

3n < 42 // Add 30 to both sides

n < 14 // Divide both sides by 3

So the inequality is true for n < 14. This means that the only integer in the set S that satisfies the inequality is 11. Therefore, the solution is S:{11}.