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10\left(-\frac{6}{5}\right)=x
Multiply both sides by -\frac{6}{5}, the reciprocal of -\frac{5}{6}.
\frac{10\left(-6\right)}{5}=x
Express 10\left(-\frac{6}{5}\right) as a single fraction.
\frac{-60}{5}=x
Multiply 10 and -6 to get -60.
-12=x
Divide -60 by 5 to get -12.
x=-12
Swap sides so that all variable terms are on the left hand side.