Question 9489
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 = 1/3 }}} <----- turned out positive since you ended up dividing two negative numbers.


{{{ abs(10 - 3(1/3)) = abs(10 - 1) = abs(9) = 9 }}} 


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


{{{ -10 + 3z = 9 }}}


{{{ 3z = 19 }}}


{{{ z = 19/3 }}} <----- 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(10 - 3(19/3)) = abs(10 - 19) = abs(-9) = 9 }}}