Question

city | temperature (°f)
a | -15
b | 22
c | -32
d | -4
e | 42
(a) compare the temperatures of city a and city d using <, >, or =. -15 < -4
what is the meaning of the inequality above?

• at 6 a.m., city a was warmer than city d.
• at 6 a.m., city a was colder than city d.

(b) compare the temperatures of city b and city c using <, >, or =. 22 > -32
what is the meaning of the inequality above?

• at 6 a.m., city c was warmer than city b.
• at 6 a.m., city c was colder than city b.

Explanation:

Part (a)

Step1: Recall number line order

On a number line, smaller numbers (more negative) are to the left of larger numbers. So, \(-15\) is left of \(-4\), meaning \(-15 < -4\).

Step2: Interpret inequality meaning

The inequality \(-15 < -4\) means City A's temperature (\(-15^\circ\text{F}\)) is less than City D's temperature (\(-4^\circ\text{F}\)). Since lower temperature means colder, City A is colder than City D. So the correct option is "At 6 a.m., City A was colder than City D."

Step1: Recall number line order

Positive numbers are greater than negative numbers. \(22\) is positive, \(-32\) is negative. So \(22 > -32\).

Step2: Interpret inequality meaning

The inequality \(22 > -32\) means City B's temperature (\(22^\circ\text{F}\)) is greater than City C's temperature (\(-32^\circ\text{F}\)). Since greater temperature means warmer, City B is warmer than City C, so City C is colder than City B. So the correct option is "At 6 a.m., City C was colder than City B."

Answer:

At 6 a.m., City A was colder than City D.

Part (b)