Question

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

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.

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.

$6000\leq x\leq 20000$

Average of 6000 and 20000 is

$\dfrac{6000+20000}{2}=13000$

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 $|x-13000|\leq 7000$.