The earth is made up of four primary layers: the inner core, outer core, mantle, and crust.The outer core is more than 800 miles and less than 2,200 miles from the Earth's center. Which of the following inequalities represents all possible distances, d, in miles, from the Earth's center that are in the outer core?

Options

A. `|d+800|lt2,200`
B. `|d-800|lt2,200`
C. `|d+1,500|lt700`
D. `|d-1,500|lt700`

Explanation

To solve the problem, we need to represent the distance \( d \) from the Earth's center that corresponds to the outer core, which is between 800 miles and 2200 miles.

### Step-by-Step Solution:

1. **Identify the Range**:
The outer core is defined as being more than 800 miles and less than 2200 miles from the Earth's center. This can be expressed as:
\[ 800 < d < 2200 \]

2. **Rearranging the Inequalities**:
We can rewrite this compound inequality into a single inequality format. It can be expressed as:
\[ d > 800 \quad \text{and} \quad d < 2200 \]

3. **Finding the Midpoint**:
To express this in terms of a central point, we can find the midpoint of the range:
\[ \text{Midpoint} = \frac{800 + 2200}{2} = 1500 \]

4. **Determining the Distance from the Midpoint**:
The distance from the midpoint (1500) to the boundaries (800 and 2200) is:
- From 1500 to 800: \( 1500 - 800 = 700 \)
- From 1500 to 2200: \( 2200 - 1500 = 700 \)

5. **Expressing the Range with Absolute Value**:
We can express the distance \( d \) in terms of its deviation from the midpoint:
\[ |d - 1500| < 700 \]

6. **Final Inequality**:
Thus, the inequality that represents all possible distances \( d \) in miles from the Earth's center that are in the outer core is:
\[ |d - 1500| < 700 \]

### Conclusion:
The correct inequality that represents the distances from the Earth's center that fall within the outer core is:
\[ |d - 1500| < 700 \]