Final answer:
To solve the inequality 3 > 11 + k/4 ≥ -3, we can break it into two separate inequalities: 11 + k/4 < 3 and 11 + k/4 ≥ -3. By solving each inequality, we find that the solution set is -56 ≤ k < -32.
Step-by-step explanation:
To solve the inequality and find the solution set:
3 > 11 + k/4 ≥ -3
We can solve this inequality by breaking it into two separate inequalities and solving each one:
11 + k/4 < 3
and
11 + k/4 ≥ -3
Solving the first inequality:
11 + k/4 < 3
Subtracting 11 from both sides:
k/4 < -8
Multiplying both sides by 4:
k < -32
The solution set for this inequality is k < -32.
Solving the second inequality:
11 + k/4 ≥ -3
Subtracting 11 from both sides:
k/4 ≥ -14
Multiplying both sides by 4:
k ≥ -56
The solution set for this inequality is k ≥ -56.
Combining the solution sets for the two inequalities, we get:
-56 ≤ k < -32
Therefore, the solution set to the inequality is -56 ≤ k < -32.