Final answer:
After solving the inequalities x + 1 < -2 and x + 11 < 3x + 5 separately, it becomes apparent that no value of x can satisfy both conditions simultaneously. Therefore, the solution set for the compound inequality is 'No solution'.
Step-by-step explanation:
The solution set of the compound inequality x + 1 < –2 and x + 11 < 3x + 5 can be found by solving each inequality separately.
For the first inequality:
- x + 1 < -2
- x < -2 - 1
- x < -3
For the second inequality:
- x + 11 < 3x + 5
- 11 - 5 < 3x - x
- 6 < 2x
- 3 < x
Combining both inequalities, we have –3 < x and x > 3, which can't be true at the same time. Therefore, there is no solution for the compound inequality because there is no value of x that can satisfy both inequalities at once.