Question

Solve the inequality and find the solution set: 3 > 11 + k/4 ≥ -3.

a) k ≤ 12
b) -12 ≤ k ≤ 12
c) k ≥ 12
d) k < -12

Answer 1

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.