A mail clerk estimates that a package will cost f dollars to ship, where `fgt20`. His goal is for the estimate to be within 2 dollars of the actual cost to ship the package. If the mall clerk meets his goal and it costs g dollars to ship the package, which of the following inequalities represents the relationship between the estimated cost and the actual shipping cost?

Options

A. `-2ltg-flt2`
B. `ggtf+2`
C. `gltf+2`
D. `f+glt2`

Answer

To solve the problem, we need to establish the relationship between the estimated shipping cost \( f \) and the actual shipping cost \( g \), given that the estimate is within 2 dollars of the actual cost.

### Step-by-Step Solution:

1. **Understanding the Given Information:**
- The estimated cost to ship a package is \( f \) dollars, where \( f > 20 \).
- The actual cost to ship the package is \( g \) dollars.
- The goal is for the estimate \( f \) to be within 2 dollars of the actual cost \( g \).

2. **Setting Up the Inequality:**
- The phrase "within 2 dollars" means that the difference between the estimated cost and the actual cost should be less than or equal to 2 dollars. This can be expressed mathematically as:
\[ |f - g| < 2 \]

3. **Breaking Down the Absolute Value Inequality:**
- The absolute value inequality \( |f - g| < 2 \) can be split into two separate inequalities:
\[ -2 < f - g < 2 \]
- This means:
\[ f - g < 2 \quad \text{and} \quad f - g > -2 \]

4. **Rearranging the Inequalities:**
- From \( f - g < 2 \):
\[ g > f - 2 \]
- From \( f - g > -2 \):
\[ g < f + 2 \]

5. **Combining the Results:**
- Combining both inequalities gives us:
\[ f - 2 < g < f + 2 \]
- This means that \( g \) must lie between \( f - 2 \) and \( f + 2 \).

6. **Final Inequality Representation:**
- The combined inequality can be expressed as:
\[ -2 < g - f < 2 \]
- This indicates that the actual cost \( g \) is within 2 dollars of the estimated cost \( f \).

### Conclusion:
The inequality that represents the relationship between the estimated cost \( f \) and the actual shipping cost \( g \) is:
\[ -2 < g - f < 2 \]
This can also be rewritten as:
\[ f - 2 < g < f + 2 \]