Answer:
S: {11}
Explanation:
Step 1: Distribute 6 to (n - 5) and 3 to (n + 4):
6 * n + 6 * -5 < 3 * n + 3 * 4
6n - 30 < 3n + 12
Step 2: Add 30 to both sides:
(6n - 30 < 3n + 12) + 30
6n < 3n + 42
Step 3: Subtract 3n from both sides:
(6n < 3n + 42) - 3n
3n < 42
Step 4: Divide both sides by 3 to determine which integer makes the inequality 6(n - 5) < 3(n + 4) true:
(3n < 42) / 3
n < 14
Thus, any integer less than 14 makes the integer true.
Since 11 is less than 14, it makes the inequality true.
Optional Step 5: Check the validity of the answer:
We can check that our answer is correct by plugging in 11 for n and seeing whether the answer on the left side is less than the answer on the right side:
6(11 - 5) < 3(11 + 4)
6(6) < 3(15)
36 < 45
Since 36 is less than 45, our answer is correct.