Question

Whcih absolute value equation could someone use to find the highest and lowest cost of a year in college?

The average cost of a year in college varies from $6000 to $20,000 depending on which college you attend.

Answer 1

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.

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.

`6000\leq x\leq 20000`

Average of 6000 and 20000 is

`(6000+20000)/(2)=13000`

Subtract average of 6000 and 20000 from each side.

`6000-13000\leq x-13000\leq 20000-13000`

`-7000\leq x-13000\leq 7000`

`|x-13000|\leq 7000`
`[\because -a\leq x\leq a\Leftrightarrow |x|\leq a]`

Therefore, the required absolute value equation is
`|x-13000|\leq 7000`.