The Formula For Converting Fahrenheit Temperatures To Celsius Temperatures Is C= 5 9 (F−32). Use This Formula For Exercises 85 And 86. During A Recent Year, The Temperatures In Chicago Ranged From −29∘ To 35∘C. Use A Compound Inequality To Convert These Temperatures To Fahrenheit Temperatures.

Video Transcript

in this problem, we're given the equation that relates the degrees and Fahrenheit to the degrees and Celsius. And we're told that the temperature range for Chicago in a particular year was from negative 29 degrees Celsius to positive 35 degrees Celsius. And we want to use an inequality to convert that into degrees Fahrenheit. So what we're going to do is take our inequality here and substitute 5/9 times F minus 32 in Percy. So that gives us negative. 29 is less than or equal to 5/9 times F minus 32 which is less than or equal to 35. And now we went to isolate F in the middle. So to undo the multiplying by 5/9 let's multiply all three parts by 9/5. When we multiply a negative 29 by 9/5 we get negative to 61 5th and in the middle are five nights is canceling the 9/5. So we're left with F minus 32 and then when we multiply 35 by 9/5 we get 63 and then the next thing we want to do is add 30 to toe all three parts to get the F by itself. So when we add 32 to the left side, we end up with negative 20.2 and then in the middle we have f, and then when we had 32 to the right side, we get 95. So what that's telling us is that the temperature range in Chicago in degrees Fahrenheit would go from negative 20.2 degrees to 95 degrees.