Sophie updated the settings on her weather app to alert her when the temperature drops below 0°C or rises above 5°C. The compoun
d inequality below translates Sophie's settings into degrees Fahrenheit. Solve the inequality and use the solution to graph the equivalent Fahrenheit temperature ranges for which Sophie will receive alerts.
2 answers:
The <u>correct solution</u> is:
x < 32 or x > 41
and the graph is attached.
Explanation:
The inequality to convert the degrees Celsius to Fahrenheit would be:
x < 9/5(0)+32 or x > 9/5(5)+32
Simplifying this, we have:
x < 0+32 or x > 45/5 + 32
x < 32 or x > 9+32
x < 32 or x > 41
To graph this, we start with a number line (in this case, from 30 to 45).
We graph an open dot at 32 and 41; the dots are open because these are not included in the solution. She wants to know when the temperature is less than 32 or greater than 41, not equal to.
From 32, we graph the line to the left, because it is less than.
From 41, we graph the line to the right, because it is greater than.
x < 32 or x > 41
and the graph is attached.
Explanation:
The inequality to convert the degrees Celsius to Fahrenheit would be:
x < 9/5(0)+32 or x > 9/5(5)+32
Simplifying this, we have:
x < 0+32 or x > 45/5 + 32
x < 32 or x > 9+32
x < 32 or x > 41
To graph this, we start with a number line (in this case, from 30 to 45).
We graph an open dot at 32 and 41; the dots are open because these are not included in the solution. She wants to know when the temperature is less than 32 or greater than 41, not equal to.
From 32, we graph the line to the left, because it is less than.
From 41, we graph the line to the right, because it is greater than.
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Step-by-step explanation:
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Using graphing technology, (see the graph) they intersect at x≈-1 and x≈8.1
