Answer :
We are given that Chicago’s temperature is
[tex]$$T_{\text{Chicago}} = -10^\circ \text{F}$$[/tex]
and that Minneapolis is colder than Chicago. This means that the temperature in Minneapolis, say
[tex]$$T_{\text{Minneapolis}},$$[/tex]
must satisfy the inequality
[tex]$$T_{\text{Minneapolis}} < -10^\circ \text{F}.$$[/tex]
We have the following candidate temperatures for Minneapolis:
[tex]$$12^\circ \text{F}, \quad 8^\circ \text{F}, \quad -8^\circ \text{F}, \quad -12^\circ \text{F}, \quad -20^\circ \text{F}.$$[/tex]
Now, we check each candidate against the condition:
1. For [tex]$12^\circ \text{F}$[/tex]:
[tex]$$12 > -10,$$[/tex]
so [tex]$12^\circ \text{F}$[/tex] is not a valid option.
2. For [tex]$8^\circ \text{F}$[/tex]:
[tex]$$8 > -10,$$[/tex]
thus [tex]$8^\circ \text{F}$[/tex] is not valid.
3. For [tex]$-8^\circ \text{F}$[/tex]:
[tex]$$-8 > -10,$$[/tex]
so [tex]$-8^\circ \text{F}$[/tex] is also not valid.
4. For [tex]$-12^\circ \text{F}$[/tex]:
[tex]$$-12 < -10,$$[/tex]
which satisfies the condition. Therefore, [tex]$-12^\circ \text{F}$[/tex] is a valid choice.
5. For [tex]$-20^\circ \text{F}$[/tex]:
[tex]$$-20 < -10,$$[/tex]
which also satisfies the condition. So, [tex]$-20^\circ \text{F}$[/tex] is a valid option.
Thus, the temperatures in Minneapolis that are colder than Chicago are
[tex]$$-12^\circ \text{F} \quad \text{and} \quad -20^\circ \text{F}.$$[/tex]
[tex]$$T_{\text{Chicago}} = -10^\circ \text{F}$$[/tex]
and that Minneapolis is colder than Chicago. This means that the temperature in Minneapolis, say
[tex]$$T_{\text{Minneapolis}},$$[/tex]
must satisfy the inequality
[tex]$$T_{\text{Minneapolis}} < -10^\circ \text{F}.$$[/tex]
We have the following candidate temperatures for Minneapolis:
[tex]$$12^\circ \text{F}, \quad 8^\circ \text{F}, \quad -8^\circ \text{F}, \quad -12^\circ \text{F}, \quad -20^\circ \text{F}.$$[/tex]
Now, we check each candidate against the condition:
1. For [tex]$12^\circ \text{F}$[/tex]:
[tex]$$12 > -10,$$[/tex]
so [tex]$12^\circ \text{F}$[/tex] is not a valid option.
2. For [tex]$8^\circ \text{F}$[/tex]:
[tex]$$8 > -10,$$[/tex]
thus [tex]$8^\circ \text{F}$[/tex] is not valid.
3. For [tex]$-8^\circ \text{F}$[/tex]:
[tex]$$-8 > -10,$$[/tex]
so [tex]$-8^\circ \text{F}$[/tex] is also not valid.
4. For [tex]$-12^\circ \text{F}$[/tex]:
[tex]$$-12 < -10,$$[/tex]
which satisfies the condition. Therefore, [tex]$-12^\circ \text{F}$[/tex] is a valid choice.
5. For [tex]$-20^\circ \text{F}$[/tex]:
[tex]$$-20 < -10,$$[/tex]
which also satisfies the condition. So, [tex]$-20^\circ \text{F}$[/tex] is a valid option.
Thus, the temperatures in Minneapolis that are colder than Chicago are
[tex]$$-12^\circ \text{F} \quad \text{and} \quad -20^\circ \text{F}.$$[/tex]
