To solve the double inequality 18 < 3n < 20 < 4n, we need to break it down into two separate inequalities and solve them one at a time.
1. First, let’s solve the part 18 < 3n:
- Divide both sides by 3:
- 6 < n
2. Now, let’s solve the part 20 < 4n:
- Again, divide both sides by 4:
- 5 < n
3. Now we need to combine our findings:
- From the first part, we have n > 6.
- From the second part, we have n > 5.
Since n > 6 is more restrictive, we only need to consider this condition. Thus, the solution set for the inequality 18 < 3n < 20 < 4n is:
- n > 6
In conclusion, the solution set is all values of n that are greater than 6.