A truck driver is driving from Nome, Alaska to Death Valley, California. Because he is traveling between locations with extreme temperatures, he needs to check the weather continuously to make sure the gas in his truck remains in liquid form. The gas he uses freezes at −40° F and evaporates at 140° F. . . Part A: Write an inequality to represent the temperatures at which the gas in the truck will remain in liquid form. (2 points) . . Part B: Describe the graph of the inequality completely from Part A. Use terms such as open/closed circles and shading directions. Explain what the solutions to the inequality represent. (4 points) . . Part C: In January 1989, the temperature in Nome, Alaska dropped to −49° F. Would the gas in the driver's truck have remained in liquid form so he could have driven on this day? Why or why not?

Part A. The inequality is   -40 < x < 140  where x is the temperature in degrees Fahrenheit. This says that x is between -40 and 140, excluding both endpoints. The value of x cannot equal either endpoint.

Part B. The graph will involve a number line, and will have two open circles at -40 and 140, with shading in between those two open circles. The open circles tell the reader to not include the endpoints. Think of them as holes in the road where the truck can't drive, whereas the shaded region is filled in pavement. Anything in the shaded region represents an x value that makes   -40 < x < 140   to be true.

Part C. Since the value -49 is smaller than -40, this means we have a temperature that is too cold to handle. The liquid gas will freeze, which makes driving the truck impossible. On the number line, -49 is to the left of -40. In other words, -49 is further from zero compared to the distance from -40 to zero.

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