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-\frac{10}{9}x-8=0
Swap sides so that all variable terms are on the left hand side.
-\frac{10}{9}x=8
Add 8 to both sides. Anything plus zero gives itself.
x=8\left(-\frac{9}{10}\right)
Multiply both sides by -\frac{9}{10}, the reciprocal of -\frac{10}{9}.
x=\frac{8\left(-9\right)}{10}
Express 8\left(-\frac{9}{10}\right) as a single fraction.
x=\frac{-72}{10}
Multiply 8 and -9 to get -72.
x=-\frac{36}{5}
Reduce the fraction \frac{-72}{10} to lowest terms by extracting and canceling out 2.