In certain greenhouse for plants, the Fahrenheit temperature, F, is controlled so that it does not vary from `79^(@)` by more than `7^(@)`. Which of the following best expresses the possible range in Fahrenheit temperature of the greenhouse?

Options

A. `|F-79|le7`
B. `|F-79|gt7`
C. `|F-7|le79`
D. `|F-7|gt79`

Answer

To find the possible range of Fahrenheit temperature \( F \) in the greenhouse, we start by interpreting the information given in the problem.

1. **Understanding the Variation**: The temperature \( F \) is controlled so that it does not vary from \( 79^\circ \) by more than \( 7^\circ \). This means that the temperature can be as low as \( 79 - 7 \) and as high as \( 79 + 7 \).

2. **Setting Up the Inequalities**:
- The maximum temperature can be expressed as:
\[ F \leq 79 + 7 \]
- The minimum temperature can be expressed as:
\[ F \geq 79 - 7 \]

3. **Calculating the Limits**:
- Calculate the maximum temperature:
\[ F \leq 79 + 7 = 86 \]
- Calculate the minimum temperature:
\[ F \geq 79 - 7 = 72 \]

4. **Combining the Inequalities**:
- We can combine the inequalities to express the range of \( F \):
\[ 72 \leq F \leq 86 \]

5. **Expressing in Absolute Value Terms**:
- We can also express this range using absolute value notation. The statement \( F \) is within \( 7 \) degrees of \( 79 \) can be written as:
\[ |F - 79| \leq 7 \]

Thus, the possible range in Fahrenheit temperature of the greenhouse is:
\[ |F - 79| \leq 7 \]