z - (-9) is the same as z + 9. Subtracting a negative is the same as adding.
Therefore
17 = z - (-9)
is the same as
17 = z + 9
To get 'z' all by itself, we need to subtract 9 from both sides. We subtract 9 from both sides to undo the "plus 9" occurring to the 'z' on the right side.
17 = z + 9
17-9 = z + 9=9 ... subtracting 9 from both sides
8 = z
z = 8
So the answer is z = 8
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Check:
17 = z - (-9)
17 = 8 - (-9) ... replace z with 8
17 = 8 + 9
17 = 17
Answer checks out
