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|z-5|-6=-3
The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -3 is 3.
|z-5|=-3+6
Add 6 to both sides.
|z-5|=3
Add -3 and 6 to get 3.
z-5=3 z-5=-3
Use the definition of absolute value.
z=8 z=2
Add 5 to both sides of the equation.