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2x-3=8-2x-\left(-2\right)
To find the opposite of 2x-2, find the opposite of each term.
2x-3=8-2x+2
The opposite of -2 is 2.
2x-3=10-2x
Add 8 and 2 to get 10.
2x-3+2x=10
Add 2x to both sides.
4x-3=10
Combine 2x and 2x to get 4x.
4x=10+3
Add 3 to both sides.
4x=13
Add 10 and 3 to get 13.
x=\frac{13}{4}
Divide both sides by 4.