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\frac{2}{3}x+8=\frac{6}{5}x
Anything divided by one gives itself.
\frac{2}{3}x+8-\frac{6}{5}x=0
Subtract \frac{6}{5}x from both sides.
-\frac{8}{15}x+8=0
Combine \frac{2}{3}x and -\frac{6}{5}x to get -\frac{8}{15}x.
-\frac{8}{15}x=-8
Subtract 8 from both sides. Anything subtracted from zero gives its negation.
x=-8\left(-\frac{15}{8}\right)
Multiply both sides by -\frac{15}{8}, the reciprocal of -\frac{8}{15}.
x=15
Multiply -8 times -\frac{15}{8}.