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Solve the following compound inequality:

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

User Ndberg
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1 Answer

4 votes

Answer:

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.

User Philippe Plantier
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