Question

In January. The temperature in Fargo, North Dakota is -2 F. On the same day, the temperature in Cheyenne, Wyoming was 1 F. Write an inequality to compare the temperatures and then write an inequality to compare the absolute values of the temperatures.

Answer 1

(a)
`1 > -2` or
`-2 < 1`

(b)
`2 > 1` or
`1 < 2`

Explanation:

Given

`N = -2F` --- North Dakota

`C = 1F` --- Cheyenne, Wyoming

Solving (a): Inequality to compare both temperatures

From the given temperatures, we can conclude that:

`C > N` or
`N < C`

Because

`1 > -2` i.e. 1 is greater than -2

or

`-2 < 1` i.e. -2 is less than 1

Solving (b): Inequality to compare the absolute values of the temperatures

We have:

`N = -2F`

`C = 1F`

The absolute values are:

`|N| = |-2|`

`|N| =2`

`|C| = |1|`

`|C| = 1`

By comparison:

`|N| > |C|` or
`|C| < |N|`

Because

`2 > 1` i.e. 2 is greater than 1

or

`1 < 2` i.e. 1 is less than 2