Final answer:
The correct compound inequality for the area written in terms of x is option (b) 100≥18x≥1,000, which simplifies to a realistic range for x between approximately 5.56 and 55.56.
Step-by-step explanation:
To choose the correct compound inequality for the area written in terms of x, we first need to understand what a compound inequality is. It is an inequality that combines two simple inequalities joined by either 'and' or 'or'. In the context of this question, we are looking for a range of values for x that make the area fall within a certain interval.
Option (a) presents the inequality 100≤10+8x≥1,000, which does not make sense as the area cannot exceed 1,000 if starting with 10 and adding 8 times x. It's also unlikely that a common compound inequality would be structured this way.
Option (b) offers the inequality 100≥18x≥1,000. This simplifies to 5.56≤x≤55.56 when divided by 18, showing a realistic range for x where the area is between 100 and 1,000.
Option (c) and (d) have similar forms to option (b), but they don't simplify to a range that would be typical for a standard problem on inequality. Therefore, we can deduce that the correct answer is option (b).