Question

Solve for a. a - 14 ≥ -4 or a + 17 ≤ -1. Write your answer as a compound inequality with integers.

A. -13 ≤ a ≤ 16
B. a ≥ -13 or a ≤ 16
C. a ≤ -13 and a ≥ 16
D. a ≥ -13 and a ≤ 16

Answer 1

None of the provided answer choices correctly match the solution of the compound inequality a - 14 ≥ -4 or a + 17 ≤ -1 which results in a ≥ 10 or a ≤ -18. Please check for any errors in the options or the original question.

Step-by-step explanation:

To solve the compound inequality a - 14 ≥ -4 or a + 17 ≤ -1 we can split it into two separate inequalities and solve each one:

1. For the first inequality, add 14 to both sides:
   
2. For the second inequality, subtract 17 from both sides:
   

This means a is either greater than or equal to 10, or less than or equal to -18. Turning this into a compound inequality, we get that the solution is a ≥ 10 or a ≤ -18. However, this does not correspond to any of the answer choices provided in the question.

Reviewing the student's options, we see that none of these options match the correct solution. If there's been an error in the provided choices or the original inequalities, it should be addressed.