Given that:
The average cost of a year in college varies from $6000 to $20,000 depending on which college you attend.
To find:
The absolute value equation the could someone use to find the highest and lowest cost of a year in college.
Step-by-step explanation:
Let the average cost of a year in college be x.
The average cost of a year in college varies from $6000 to $20,000.
[tex]6000\leq x\leq 20000[/tex]
Average of 6000 and 20000 is
[tex]\dfrac{6000+20000}{2}=13000[/tex]
Subtract average of 6000 and 20000 from each side.
[tex]6000-13000\leq x-13000\leq 20000-13000[/tex]
[tex]-7000\leq x-13000\leq 7000[/tex]
[tex]|x-13000|\leq 7000[/tex] [tex][\because -a\leq x\leq a\Leftrightarrow |x|\leq a][/tex]
Therefore, the required absolute value equation is [tex]|x-13000|\leq 7000[/tex].
