High School

Elena and Lin are planning some cold-weather camping and are considering their equipment:

- A down jacket is rated as comfortable when the temperature is between [tex]$-20^{\circ} F$[/tex] and [tex]$20^{\circ} F$[/tex].
- A down sleeping bag is rated as comfortable when the temperature is [tex]$-20^{\circ} F$[/tex] or above.
- A synthetic sleeping bag is rated as comfortable when the temperature is [tex]$20^{\circ} F$[/tex] or above.

The coldest month of the year in Dover is January, with an average low of [tex]$28^{\circ} F$[/tex] and high of [tex]$42^{\circ} F$[/tex].

Choose one or more inequalities representing the range of temperatures in your area in the winter:

A. [tex]$x = 28$[/tex] and [tex]$x = 42$[/tex]

B. [tex]$x \leq 42$[/tex]

C. [tex]$x \leq 28$[/tex]

D. [tex]$42 \leq x$[/tex]

E. [tex]$28 \leq x$[/tex]

Answer :

To solve the question about the range of temperatures in your area in the winter, let's break down the information and determine which inequalities apply based on the given temperatures.

### Understanding the Temperature Range:

1. Dover Winter Temperatures:
- The average low temperature in January is [tex]\(28^\circ F\)[/tex].
- The average high temperature in January is [tex]\(42^\circ F\)[/tex].

This means the temperature during winter can be any value between [tex]\(28^\circ F\)[/tex] and [tex]\(42^\circ F\)[/tex].

### Choosing Inequalities:

To represent this range using inequalities, we need conditions that reflect any temperature within this span, from the lowest to the highest.

- Choices Given:
- [tex]\(x = 28\)[/tex] and [tex]\(x = 42\)[/tex]
- [tex]\(x \leq 42\)[/tex]
- [tex]\(x \leq 28\)[/tex]
- [tex]\(42 \leq x\)[/tex]
- [tex]\(28 \leq x\)[/tex]

#### Evaluating the Choices:

1. [tex]\(x \leq 42\)[/tex]:
- This inequality states that [tex]\(x\)[/tex] can be any temperature up to [tex]\(42^\circ F\)[/tex], which is correct for our range because the maximum average temperature is [tex]\(42^\circ F\)[/tex].

2. [tex]\(x \leq 28\)[/tex]:
- This inequality limits [tex]\(x\)[/tex] to temperatures [tex]\(28^\circ F\)[/tex] or below, which does not fit our range; we expect temperatures to go above [tex]\(28^\circ F\)[/tex].

3. [tex]\(42 \leq x\)[/tex]:
- This suggests temperatures start at [tex]\(42^\circ F\)[/tex] or higher. This is not correct since [tex]\(42^\circ F\)[/tex] is the upper boundary of our range.

4. [tex]\(28 \leq x\)[/tex]:
- This states that [tex]\(x\)[/tex] can be any temperature from [tex]\(28^\circ F\)[/tex] upward, which correctly reflects the lower limit of our temperature range.

### Correct Inequalities:

Based on the choices, the correct inequalities that represent the range of temperatures from [tex]\(28^\circ F\)[/tex] to [tex]\(42^\circ F\)[/tex] are:

- [tex]\(x \leq 42\)[/tex] (temperature can go up to [tex]\(42^\circ F\)[/tex])
- [tex]\(28 \leq x\)[/tex] (temperature can start from [tex]\(28^\circ F\)[/tex])

Together, these inequalities can also be combined to explicitly express the full range as:
- [tex]\(28 \leq x \leq 42\)[/tex]

This means that the temperature, [tex]\(x\)[/tex], is at least [tex]\(28^\circ F\)[/tex] and at most [tex]\(42^\circ F\)[/tex], which fits our winter temperature data perfectly.