Final answer:
After evaluating each inequality by substituting x with 4, we find that inequalities a and d include 4 in their solution sets because the resulting expressions are true when x is 4.
Step-by-step explanation:
The student has asked which inequalities include 4 in the solution set. To determine if 4 is a solution, we need to substitute x = 4 into each inequality and see if it makes the inequality true.
- For inequality a, x - 6 < 9, substituting x with 4 gives us 4 - 6 < 9, which simplifies to -2 < 9. This is true, so 4 is included in the solution set.
- For inequality b, -1 > 3x + 8, substituting x with 4 gives us -1 > 3(4) + 8, which simplifies to -1 > 20. This is false, so 4 is not included in the solution set.
- For inequality c, 5x < 20, substituting x with 4 gives us 5(4) < 20, which simplifies to 20 < 20. This is false as the inequality is strict (<), so 4 is not included in the solution set.
- For inequality d, 3 + 2x < 11, substituting x with 4 gives us 3 + 2(4) < 11, which simplifies to 3 + 8 < 11. This is true, and therefore 4 is included in the solution set.
Thus, the inequalities that include 4 in the solution set are a and d.