SOLUTION: I have been racking my brain for 2 days trying to answer this equation, but with no avail... |10 - 3z| = 9 I keep getting fractions and mixed numbers (such as 6 1/3 and -1/3

Algebra ->  Absolute-value -> SOLUTION: I have been racking my brain for 2 days trying to answer this equation, but with no avail... |10 - 3z| = 9 I keep getting fractions and mixed numbers (such as 6 1/3 and -1/3       Log On


   

Question 9489: I have been racking my brain for 2 days trying to answer this equation, but with no avail...
|10 - 3z| = 9
I keep getting fractions and mixed numbers (such as 6 1/3 and -1/3 for z) for answers and when I plug them back in the equation, they're never right. Can you please help me?
Thanks,
Laura
Answer by prince_abubu(198) About Me  (Show Source):
You can put this solution on YOUR website!
When you see absolute value signs like this, you know that you have to solve two equations.

I: As is, just take off the absolute value signs.

+10+-+3z+=+9+

+-3z+=+-1+

+z+=+1%2F3+ <----- turned out positive since you ended up dividing two negative numbers.

+abs%2810+-+3%281%2F3%29%29+=+abs%2810+-+1%29+=+abs%289%29+=+9+

-----------------------------------------
Case 2: Flip the signs of the terms inside the absolute value

+-10+%2B+3z+=+9+

+3z+=+19+

+z+=+19%2F3+ <----- 19/3 is the same as 6 1/3. We're gonna keep it as an improper fraction, since it's easier to calculate with. Let's check

+abs%2810+-+3%2819%2F3%29%29+=+abs%2810+-+19%29+=+abs%28-9%29+=+9+