Solved on Dec 15, 2023

Find the temperature range that Andrew considers comfortable. Write an absolute value equation to represent the situation, then solve for the minimum and maximum temperatures.
Part A: $|T - 70^{\circ} \mathrm{F}| \leq 5^{\circ} \mathrm{F}$ Part B: Minimum: $65^{\circ} \mathrm{F}$ , Maximum: $75^{\circ} \mathrm{F}$

STEP 1

Assumptions
1. Andrew wants the temperature to be $70^{\circ}F$ .
2. The temperature can vary by plus or minus 5 degrees.
3. We need to write an absolute value equation to represent the situation.
4. We need to solve the equation to find the minimum and maximum temperatures.

STEP 2

Part A requires us to write an absolute value equation. The absolute value of a number represents its distance from zero on the number line, regardless of direction. In this case, the distance from the desired temperature ( $70^{\circ}F$ ) can be at most 5 degrees in either direction.
$|Temperature - Desired\, Temperature| = Maximum\, Variation$

STEP 3

Now, plug in the values for the desired temperature and the maximum variation to create the equation.
$|Temperature - 70^{\circ}F| = 5^{\circ}F$

STEP 4

This is the absolute value equation that represents the situation.
$|T - 70| = 5$
Where $T$ is the actual temperature of Andrew's apartment.

STEP 5

Part B requires us to solve the absolute value equation to find the minimum and maximum temperatures.
An absolute value equation $|x| = a$ has two solutions: $x = a$ and $x = -a$ . Applying this to our equation:
$T - 70 = 5 \quad \text{or} \quad T - 70 = -5$

STEP 6

First, solve the equation where the temperature is 5 degrees more than the desired temperature.
$T - 70 = 5$

STEP 7

Add 70 to both sides of the equation to solve for $T$ .
$T = 5 + 70$

STEP 8

Calculate the value of $T$ .
$T = 75$
This is the maximum temperature for Andrew's apartment.

STEP 9

Now, solve the equation where the temperature is 5 degrees less than the desired temperature.
$T - 70 = -5$

STEP 10

Add 70 to both sides of the equation to solve for $T$ .
$T = -5 + 70$

STEP 11

Calculate the value of $T$ .
$T = 65$
This is the minimum temperature for Andrew's apartment.
Minimum: $65^{\circ}F$ Maximum: $75^{\circ}F$

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STEP 1

Assumptions
1. Andrew wants the temperature to be $70^{\circ}F$ .
2. The temperature can vary by plus or minus 5 degrees.
3. We need to write an absolute value equation to represent the situation.
4. We need to solve the equation to find the minimum and maximum temperatures.

STEP 2

STEP 3

Now, plug in the values for the desired temperature and the maximum variation to create the equation.
$|Temperature - 70^{\circ}F| = 5^{\circ}F$

STEP 4

This is the absolute value equation that represents the situation.
$|T - 70| = 5$
Where $T$ is the actual temperature of Andrew's apartment.

STEP 5

Part B requires us to solve the absolute value equation to find the minimum and maximum temperatures.
An absolute value equation $|x| = a$ has two solutions: $x = a$ and $x = -a$ . Applying this to our equation:
$T - 70 = 5 \quad \text{or} \quad T - 70 = -5$

STEP 6

First, solve the equation where the temperature is 5 degrees more than the desired temperature.
$T - 70 = 5$

STEP 7

Add 70 to both sides of the equation to solve for $T$ .
$T = 5 + 70$

STEP 8

Calculate the value of $T$ .
$T = 75$
This is the maximum temperature for Andrew's apartment.

STEP 9

Now, solve the equation where the temperature is 5 degrees less than the desired temperature.
$T - 70 = -5$

STEP 10

Add 70 to both sides of the equation to solve for $T$ .
$T = -5 + 70$

STEP 11

Calculate the value of $T$ .
$T = 65$
This is the minimum temperature for Andrew's apartment.
Minimum: $65^{\circ}F$ Maximum: $75^{\circ}F$

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STEP 1

Assumptions1. Andrew wants the temperature to be 70∘F70^{\circ}F70∘F.2. The temperature can vary by plus or minus 5 degrees.3. We need to write an absolute value equation to represent the situation.4. We need to solve the equation to find the minimum and maximum temperatures.

STEP 2

STEP 3

Now, plug in the values for the desired temperature and the maximum variation to create the equation.∣Temperature−70∘F∣=5∘F|Temperature - 70^{\circ}F| = 5^{\circ}F∣Temperature−70∘F∣=5∘F

STEP 4

This is the absolute value equation that represents the situation.∣T−70∣=5|T - 70| = 5∣T−70∣=5Where TTT is the actual temperature of Andrew's apartment.

STEP 5

STEP 6

First, solve the equation where the temperature is 5 degrees more than the desired temperature.T−70=5T - 70 = 5T−70=5

STEP 7

Add 70 to both sides of the equation to solve for TTT.T=5+70T = 5 + 70T=5+70

STEP 8

Calculate the value of TTT.T=75T = 75T=75This is the maximum temperature for Andrew's apartment.

STEP 9

Now, solve the equation where the temperature is 5 degrees less than the desired temperature.T−70=−5T - 70 = -5T−70=−5

STEP 10

Add 70 to both sides of the equation to solve for TTT.T=−5+70T = -5 + 70T=−5+70

STEP 11

Calculate the value of TTT.T=65T = 65T=65This is the minimum temperature for Andrew's apartment.Minimum: 65∘F65^{\circ}F65∘F Maximum: 75∘F75^{\circ}F75∘F

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Assumptions
1. Andrew wants the temperature to be $70^{\circ}F$ .
2. The temperature can vary by plus or minus 5 degrees.
3. We need to write an absolute value equation to represent the situation.
4. We need to solve the equation to find the minimum and maximum temperatures.

Now, plug in the values for the desired temperature and the maximum variation to create the equation.
$|Temperature - 70^{\circ}F| = 5^{\circ}F$

This is the absolute value equation that represents the situation.
$|T - 70| = 5$
Where $T$ is the actual temperature of Andrew's apartment.

First, solve the equation where the temperature is 5 degrees more than the desired temperature.
$T - 70 = 5$

Add 70 to both sides of the equation to solve for $T$ .
$T = 5 + 70$

Calculate the value of $T$ .
$T = 75$
This is the maximum temperature for Andrew's apartment.

Now, solve the equation where the temperature is 5 degrees less than the desired temperature.
$T - 70 = -5$

Add 70 to both sides of the equation to solve for $T$ .
$T = -5 + 70$

Calculate the value of $T$ .
$T = 65$
This is the minimum temperature for Andrew's apartment.
Minimum: $65^{\circ}F$ Maximum: $75^{\circ}F$