The solution to the compound inequality 5 + x < 23 or 6x + 1 < -29 is x < -5, which corresponds to answer choice a. This is because any number less than -5 will satisfy both parts of the compound inequality.
The solution to the compound inequality 5 + x < 23 or 6x + 1 < -29 involves solving each inequality separately and then combining the results:
- For the first inequality, subtract 5 from both sides to get x < 18.
- For the second inequality, subtract 1 from both sides to get 6x < -30, then divide by 6 to get x < -5.
The solution is the union of the individual solutions: x < 18 or x < -5. Since any number less than -5 is naturally less than 18, we can say the solution is x < -5, which means the correct answer is a. x < -5.