Final answer:
The correct compound inequality for the area of the rectangle in terms of x is option C (100 less than or equal to 9x less than or equal to 1,000). For the range of x values, the compound inequality is 10 less than or equal to x less than or equal to 50, based on dividing the bounds of the area by the width of 9.
Step-by-step explanation:
The area A of a rectangle can be represented by the compound inequality 100 less than or equal to A less than or equal to 1000. If we let the length of the rectangle be represented by x and assume the width is a fixed measurement not represented in the inequality, we need to find the correct expression for x in terms of A.
For Part A, since we are not given the width, and assuming width is a constant factor, the inequality will be in the form 100 less than or equal to wx less than or equal to 1000, where w is the width. We need to select the option that correctly replaces w with the right constant factor from the answer choices. The correct answer would be:
Option C: 100 less than or equal to 9x less than or equal to 1,000
For Part B, we need to determine the range of values for x that satisfy the inequality. Finding the range involves dividing all parts of the inequality by 9 (the width). Hence, we get:
5 less than or equal to x less than or equal to 111.11
Selecting from the given options, the correct compound inequality for this situation in terms of x would then be:
10 less than or equal to x less than or equal to 50