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\frac{1}{3}x+4-\frac{7}{9}x=0
Subtract \frac{7}{9}x from both sides.
-\frac{4}{9}x+4=0
Combine \frac{1}{3}x and -\frac{7}{9}x to get -\frac{4}{9}x.
-\frac{4}{9}x=-4
Subtract 4 from both sides. Anything subtracted from zero gives its negation.
x=-4\left(-\frac{9}{4}\right)
Multiply both sides by -\frac{9}{4}, the reciprocal of -\frac{4}{9}.
x=9
Multiply -4 times -\frac{9}{4}.