Answer :
To express the temperature range on Mars as an absolute value inequality, you can follow these steps:
1. Identify the Limits of the Range:
The given temperature range on Mars is from -70 degrees Fahrenheit to 220 degrees Fahrenheit.
2. Find the Midpoint of the Range:
To write an absolute value inequality, first, find the midpoint (or center) of the temperature range. This is done by averaging the two extremes of the range:
[tex]\[
\text{Midpoint} = \frac{-70 + 220}{2} = 75
\][/tex]
So, the midpoint is 75 degrees Fahrenheit.
3. Calculate the Deviation:
Next, determine how far the endpoints of the range are from this midpoint. You can use either endpoint for this calculation. We'll use 220 degrees:
[tex]\[
\text{Deviation} = 220 - 75 = 145
\][/tex]
4. Write the Absolute Value Inequality:
With the midpoint and deviation determined, you can write the absolute value inequality. The inequality represents all temperatures, [tex]\( x \)[/tex], that are within 145 degrees of 75 degrees:
[tex]\[
|x - 75| \leq 145
\][/tex]
This inequality captures the range of temperatures on Mars, meaning the actual temperature [tex]\( x \)[/tex] can be as low as -70 degrees or as high as 220 degrees.
1. Identify the Limits of the Range:
The given temperature range on Mars is from -70 degrees Fahrenheit to 220 degrees Fahrenheit.
2. Find the Midpoint of the Range:
To write an absolute value inequality, first, find the midpoint (or center) of the temperature range. This is done by averaging the two extremes of the range:
[tex]\[
\text{Midpoint} = \frac{-70 + 220}{2} = 75
\][/tex]
So, the midpoint is 75 degrees Fahrenheit.
3. Calculate the Deviation:
Next, determine how far the endpoints of the range are from this midpoint. You can use either endpoint for this calculation. We'll use 220 degrees:
[tex]\[
\text{Deviation} = 220 - 75 = 145
\][/tex]
4. Write the Absolute Value Inequality:
With the midpoint and deviation determined, you can write the absolute value inequality. The inequality represents all temperatures, [tex]\( x \)[/tex], that are within 145 degrees of 75 degrees:
[tex]\[
|x - 75| \leq 145
\][/tex]
This inequality captures the range of temperatures on Mars, meaning the actual temperature [tex]\( x \)[/tex] can be as low as -70 degrees or as high as 220 degrees.
