Let d represent the distance, in miles, that Sarah’s car will go using a full tank of gas.
Drag the words, numbers, and symbols into the boxes to complete a compound inequality that can be solved to find the range of distance Sarah's car can go using a full tank. d BLANK 15x BLANK The available boxes include is greater than or equal to, 24, AND, is less than or BLANK d BLANK 15x BLANK equal to, 32, OR, and 15. Enter numbers in the boxes that complete the simplified inequality. BLANK is less than or equal to d is less than or equal to BLANK

To construct the compound inequality that represents the range of distances Sarah's car can travel using a full tank of gas, let's analyze the given elements:

1. We need to relate `d`, the distance Sarah's car can travel, to `15x` and the numbers 24 and 32.
2. We want to form a compound inequality that expresses the range of possible distances using the provided options.

**Available boxes include:**
- is greater than or equal to
- 24
- AND
- is less than or
- 15
- equal to
- 32
- OR

**Goal:**
- Complete the inequality: BLANK is less than or equal to `d` is less than or equal to BLANK.

### Step-by-Step Construction:

1. We know that the expression should be in the form of:
   \[
   \text{(lower bound)} \leq d \leq \text{(upper bound)}
   \]
   
2. From the provided options, the numbers that would logically set the boundaries are 24 and 32 because they are given as distinct numbers to work with.

3. The problem can be interpreted to define a range for `d` between these two numbers.

### Filling in the Inequality:

- The smallest number given for the lower bound is **24**.
- The largest number given for the upper bound is **32**.

Thus, the compound inequality becomes:

\[
24 \ \text{is less than or equal to} \ d \ \text{is less than or equal to} \ 32
\]

This correctly represents the range of distances Sarah's car can travel using a full tank of gas.

**Would you like more details or have any other questions?**

Here are five related questions to expand on this topic:

1. What does the inequality tell us about the minimum and maximum distances Sarah's car can travel?
2. How would the inequality change if the lower bound was set to 15 instead of 24?
3. If `d = 28`, does it satisfy the inequality?
4. How can this inequality be graphically represented on a number line?
5. What if the fuel efficiency changes to `20x` miles per tank instead of `15x`? How would that affect the inequality?

**Tip:** When interpreting inequalities, make sure to understand what each symbol and number represents in context to apply them correctly to real-world scenarios.

Understand how to solve a compound inequality to determine the range of distances Sarah's car can travel using a full tank of gas. Learn step-by-step with examples and explanations. Suitable for Grades 6-8.

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