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x-7=6-x-\left(-3\right)
To find the opposite of x-3, find the opposite of each term.
x-7=6-x+3
The opposite of -3 is 3.
x-7=9-x
Add 6 and 3 to get 9.
x-7+x=9
Add x to both sides.
2x-7=9
Combine x and x to get 2x.
2x=9+7
Add 7 to both sides.
2x=16
Add 9 and 7 to get 16.
x=\frac{16}{2}
Divide both sides by 2.
x=8
Divide 16 by 2 to get 8.