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2x-\frac{2}{3}x\geq 4
Subtract \frac{2}{3}x from both sides.
\frac{4}{3}x\geq 4
Combine 2x and -\frac{2}{3}x to get \frac{4}{3}x.
x\geq 4\times \frac{3}{4}
Multiply both sides by \frac{3}{4}, the reciprocal of \frac{4}{3}. Since \frac{4}{3} is positive, the inequality direction remains the same.
x\geq 3
Cancel out 4 and 4.