Question

Solve the following compound inequality:

1 - 58 < 5 + 7n < -44
A) { All real numbers. }
B) -9
C) n < 6
D) n > 3

Answer 1

Upon solving the compound inequality 1 - 58 < 5 + 7n < -44 step by step, we find that the solution is n < -7. However, this observed solution is not one of the options provided in the question, implying that the correct answer is 'None of the above.'

Step-by-step explanation:

To solve the compound inequality 1 - 58 < 5 + 7n < -44, we need to solve two separate inequalities and then find the intersection of their solutions.

Step 1: Solve the left inequality 1 - 58 < 5 + 7n.

• First, simplify the left side:
  -57 < 5 + 7n.
• Next, subtract 5 from both sides:
  -57 - 5 < 7n.
  -62 < 7n.
• Divide by 7:
  -62 / 7 < n.
  -8.857 < n.

Step 2: Solve the right inequality 5 + 7n < -44.

• Subtract 5 from both sides:
  7n < -44 - 5.
  7n < -49.
• Divide by 7:
  n < -49 / 7.
  n < -7.

Step 3: Find the intersection of the two inequalities:
-8.857 < n < -7.

Therefore, the solution is n < -7, which corresponds to the answer choice C) n < 6 if we accept it as an approximation, but actually -7 is not less than -7, so the accurate choice reflecting our calculation is not listed among the choices, meaning the correct answer is None of the above.