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10-1x=1-9x

We move all terms to the left:

10-1x-(1-9x)=0

We add all the numbers together, and all the variables

-1x-(-9x+1)+10=0

We get rid of parentheses

-1x+9x-1+10=0

We add all the numbers together, and all the variables

8x+9=0

We move all terms containing x to the left, all other terms to the right

8x=-9

x=-9/8

x=-1+1/8

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