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\frac{2}{3}x+4=0
Swap sides so that all variable terms are on the left hand side.
\frac{2}{3}x=-4
Subtract 4 from both sides. Anything subtracted from zero gives its negation.
x=-4\times \frac{3}{2}
Multiply both sides by \frac{3}{2}, the reciprocal of \frac{2}{3}.
x=\frac{-4\times 3}{2}
Express -4\times \frac{3}{2} as a single fraction.
x=\frac{-12}{2}
Multiply -4 and 3 to get -12.
x=-6
Divide -12 by 2 to get -6.