Given:
Suppose the temperature x miles above ground level is given by
[tex]T=74-29x[/tex]
To find:
The inequality and solve the inequality that describes when the temperature is below 50 degrees F.
Solution:
The temperature is below 50 degrees F. It means the temperature is less than 50 degrees F.
[tex]T<50[/tex]
[tex]74-29x<50[/tex]
[tex]-29x<50-74[/tex]
[tex]-29x<-24[/tex]
Divide both sides by -29 and change the inequality sign.
[tex]x>\dfrac{-24}{-29}[/tex]
[tex]x>0.8275862[/tex]
[tex]x>0.828[/tex]
Therefore, the required inequality is [tex]74-29x<50[/tex] and the solution is [tex]x>0.828[/tex].
The inequality of the given situation is required to be solved.
If the miles above ground is greater than 0.828 miles then the temperature is below [tex]50^{\circ}\text{F}[/tex]
The given equation is [tex]T=74-29x[/tex]
where,
T = Temperature
x = Miles above ground level
Now if [tex]T<50^{\circ}\text{F}[/tex]
Solving the inequality
[tex]74-29x<50\\\Rightarrow -29x<50-74\\\Rightarrow 29x>24\\\Rightarrow x>\dfrac{24}{29}\\\Rightarrow x>0.828[/tex]
Learn more about inequalities:
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