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\frac{2}{3}x+1-6x=0
Subtract 6x from both sides.
-\frac{16}{3}x+1=0
Combine \frac{2}{3}x and -6x to get -\frac{16}{3}x.
-\frac{16}{3}x=-1
Subtract 1 from both sides. Anything subtracted from zero gives its negation.
x=-\left(-\frac{3}{16}\right)
Multiply both sides by -\frac{3}{16}, the reciprocal of -\frac{16}{3}.
x=\frac{3}{16}
Multiply -1 and -\frac{3}{16} to get \frac{3}{16}.