Step 1: Find the slope of AB. The slope of AB is
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The inequality to represent the temperatures at which the gas in the truck will remain in liquid form is -40 < x < 140
<h3>Part A: The inequality</h3>Let the temperature of the gas be represented with x.
When the temperature hits −40° F (or below), the gas freezes.
This means that the gas temperature must always exceed −40° F to remain being a liquid
i.e x > −40
Also, when the temperature hits 140° F (or above), the gas evaporates.
This means that the gas temperature must always be less than 140° F to remain being a liquid
i.e x < 140
So, we have:
x > −40 and x < 140
Rewrite as:
-40 < x and x < 140
Combine both inequalities
-40 < x < 140
Hence, the inequality to represent the temperatures at which the gas in the truck will remain in liquid form is -40 < x < 140
<h3>Part B: The description of the graph</h3>In (a), we have:
-40 < x < 140
The end points of the inequalities use a less than sign.
Less than signs are represented by open circle.
Hence, the graph would use an open circle, and intervals between -40 and 140 would be shaded
<h3>Part C: Would −49° F gas remained in liquid form?</h3>We have:
-40 < x < 140
The number -49 is not in the range -40 < x < 140
Hence, the gas would not remain in liquid form (in fact, it would freeze because it is less than -40)
Read more about inequalities at:
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