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x+\frac{10}{9}-\frac{8}{9}x=0
Subtract \frac{8}{9}x from both sides.
\frac{1}{9}x+\frac{10}{9}=0
Combine x and -\frac{8}{9}x to get \frac{1}{9}x.
\frac{1}{9}x=-\frac{10}{9}
Subtract \frac{10}{9} from both sides. Anything subtracted from zero gives its negation.
x=-\frac{10}{9}\times 9
Multiply both sides by 9, the reciprocal of \frac{1}{9}.
x=-10
Cancel out 9 and 9.