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x<6\times \frac{3}{2}
Multiply both sides by \frac{3}{2}, the reciprocal of \frac{2}{3}. Since \frac{2}{3} is positive, the inequality direction remains the same.
x<\frac{6\times 3}{2}
Express 6\times \frac{3}{2} as a single fraction.
x<\frac{18}{2}
Multiply 6 and 3 to get 18.
x<9
Divide 18 by 2 to get 9.