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x-1=9-x-\left(-1\right)
To find the opposite of x-1, find the opposite of each term.
x-1=9-x+1
The opposite of -1 is 1.
x-1=10-x
Add 9 and 1 to get 10.
x-1+x=10
Add x to both sides.
2x-1=10
Combine x and x to get 2x.
2x=10+1
Add 1 to both sides.
2x=11
Add 10 and 1 to get 11.
x=\frac{11}{2}
Divide both sides by 2.