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2x-3=3-2x-\left(-6\right)
To find the opposite of 2x-6, find the opposite of each term.
2x-3=3-2x+6
The opposite of -6 is 6.
2x-3=9-2x
Add 3 and 6 to get 9.
2x-3+2x=9
Add 2x to both sides.
4x-3=9
Combine 2x and 2x to get 4x.
4x=9+3
Add 3 to both sides.
4x=12
Add 9 and 3 to get 12.
x=\frac{12}{4}
Divide both sides by 4.
x=3
Divide 12 by 4 to get 3.