Question

Solve the compound inequality: -33 < -7n - 12 ≤ -26.

A. n > 3
B. n < -3
C. -3 < n ≤ 3
D. n > -3

Answer 1

To solve the compound inequality -33 < -7n - 12 ≤ -26, break it down into two separate inequalities: -33 < -7n - 12 and -7n - 12 ≤ -26. Solve each inequality separately and combine the solutions to get n < 3 and n ≥ 2, resulting in -3 < n ≤ 3.

Step-by-step explanation:

To solve the compound inequality -33 < -7n - 12 ≤ -26, we need to break it down into two separate inequalities: -33 < -7n - 12 and -7n - 12 ≤ -26.

For the first inequality, we can solve it as follows:

• -7n - 12 > -33
• -7n > -33 + 12
• -7n > -21
• n < -21/-7
• n < 3

For the second inequality, we can solve it as follows:

• -7n - 12 ≤ -26
• -7n ≤ -26 + 12
• -7n ≤ -14
• n ≥ -14/-7
• n ≥ 2

Combining the solutions, we have n < 3 and n ≥ 2.

Therefore, the solution to the compound inequality is -3 < n ≤ 3. Therefore, the correct answer is C. -3 < n ≤ 3.