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\frac{3}{2}x+1=1
Swap sides so that all variable terms are on the left hand side.
\frac{3}{2}x=1-1
Subtract 1 from both sides.
\frac{3}{2}x=0
Subtract 1 from 1 to get 0.
x=0
Product of two numbers is equal to 0 if at least one of them is 0. Since \frac{3}{2} is not equal to 0, x must be equal to 0.