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\frac{1}{5}x+6-\frac{7}{10}x=0
Subtract \frac{7}{10}x from both sides.
-\frac{1}{2}x+6=0
Combine \frac{1}{5}x and -\frac{7}{10}x to get -\frac{1}{2}x.
-\frac{1}{2}x=-6
Subtract 6 from both sides. Anything subtracted from zero gives its negation.
x=-6\left(-2\right)
Multiply both sides by -2, the reciprocal of -\frac{1}{2}.
x=12
Multiply -6 and -2 to get 12.