Final answer:
The inequality -87 < 38 is given, and the correct inequality representing the solution set is C. -87 < -38, because -87 is indeed smaller than -38 in the context of negative numbers. Therefore, the correct inequality that represents the solution set is C. -87 < -38.
Step-by-step explanation:
The given inequality is -87 < 38. This inequality indicates that -87 is less than 38. To find which inequality represents the solution set, we must determine the correct relationship between -87 and another number that keeps the inequality true.
Option A suggests that -87 is greater than 38, which is incorrect because -87 is a negative number and 38 is a positive number, and negative numbers are always less than positive numbers.
Option B suggests that -87 is greater than or equal to 38, which is also incorrect for the same reason as option A.
Option C suggests that -87 is less than -38. While both numbers are negative, -87 is indeed smaller (or further from zero) than -38.
Option D suggests that -87 is greater than -38, which is incorrect because, in the context of negative numbers, smaller numbers are actually further away from zero and hence considered 'less than' larger negative numbers.
Therefore, the correct inequality that represents the solution set is C. -87 < -38.