SOLUTION: The highest elevation in North America is 20,320 feet above sea level at mount McKinley. The lowest elevation is 282 feet below sea level in Death valley. Find an absolute value eq

Algebra ->  Inequalities -> SOLUTION: The highest elevation in North America is 20,320 feet above sea level at mount McKinley. The lowest elevation is 282 feet below sea level in Death valley. Find an absolute value eq      Log On


   



Question 175504: The highest elevation in North America is 20,320 feet above sea level at mount McKinley. The lowest elevation is 282 feet below sea level in Death valley. Find an absolute value equation that has the highest and lowest elevations in North America as its solution.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

Let the absolute value equation be this:

|x + a| = b  (where b is a non-negative number)

Then the two equations resulting from this are:

x + a = b,    x + a = -b

Let's substitute 20320 for x in the first equation
and -282 in the second equation:

20320 + a = b    -282 + a = b

So we have this system of euations:

system%2820320+%2B+a+=+b%2C+-282+%2B+a+=+-b%29

or we can write it better this way:

system%28a-b=-20320%2C+a%2Bb=282%29

Can you solve that system, either by substitution
or elimination?  If not post again
asking how.

Solution:  a = - 10019,  b = 10301

So the equation

|x + a| = b

becomes:

|x - 10019| = 10301  

Edwin