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\frac{1}{2}\times \frac{2}{3}\times 2x\times 30=90\times 18000
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 90x, the least common multiple of 2,3,45,x.
\frac{1\times 2}{2\times 3}\times 2x\times 30=90\times 18000
Multiply \frac{1}{2} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.
\frac{1}{3}\times 2x\times 30=90\times 18000
Cancel out 2 in both numerator and denominator.
\frac{2}{3}x\times 30=90\times 18000
Multiply \frac{1}{3} and 2 to get \frac{2}{3}.
\frac{2\times 30}{3}x=90\times 18000
Express \frac{2}{3}\times 30 as a single fraction.
\frac{60}{3}x=90\times 18000
Multiply 2 and 30 to get 60.
20x=90\times 18000
Divide 60 by 3 to get 20.
20x=1620000
Multiply 90 and 18000 to get 1620000.
x=\frac{1620000}{20}
Divide both sides by 20.
x=81000
Divide 1620000 by 20 to get 81000.