A certain medication must be stored at a temperature, t, that may range between a low at `45^(@)` Fahrenheit a high of `85^(@)` Fahreheit. Which inequality represents the allowable range of Fahrenheit temperature?

Options

A. `|t-65|le20`
B. `|t+20|le65`
C. `|t+65|le20`
D. `|t-20|le85`

Answer

To solve the problem, we need to express the allowable range of temperatures for the medication in terms of an inequality.

### Step-by-Step Solution:

1. **Identify the Temperature Range**:
The medication must be stored at a temperature \( t \) that ranges from a low of \( 45^\circ \) Fahrenheit to a high of \( 85^\circ \) Fahrenheit.

2. **Set Up the Inequality**:
We can express this range using inequalities:
\[ 45 \leq t \leq 85 \]

3. **Rearranging the Inequality**:
To express this in a different form, we can manipulate the inequality. We can subtract \( 65 \) from all parts of the inequality:
\[ 45 - 65 \leq t - 65 \leq 85 - 65 \]
This simplifies to:
\[ -20 \leq t - 65 \leq 20 \]

4. **Expressing in Absolute Value Form**:
The inequality \( -20 \leq t - 65 \leq 20 \) can be rewritten in absolute value notation. It states that the distance of \( t \) from \( 65 \) is at most \( 20 \):
\[ |t - 65| \leq 20 \]

5. **Final Inequality**:
Thus, the inequality that represents the allowable range of Fahrenheit temperature is:
\[ |t - 65| \leq 20 \]

### Conclusion:
The correct inequality representing the allowable range of Fahrenheit temperature is \( |t - 65| \leq 20 \).