Final answer:
The inequality representing the total number of surveys sent out, given that 84 households responded being less than one-fourth of the total, is expressed as 84 < 0.25h, implying that more than 336 surveys were sent out.
Step-by-step explanation:
The question posed requires us to identify the inequality that represents how many surveys were sent out, given that 84 households responded and this number is less than one-fourth of the total sent out. To represent this mathematically, let the variable h represent the total number of surveys sent out. We are told that 84 is less than one-fourth of the total, so the inequality is:
84 < ¼h or alternatively 84 < 0.25h.
Therefore, option B) 84 > h is incorrect because it suggests that 84 is greater than the total number of surveys, which contradicts the information given. The correct inequality is represented by multiplying both sides of the inequality by 4 to remove the fraction, which gives us 336 < h. This tells us that more than 336 surveys were sent out.