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\frac{3}{2}x-1-2x>0
Subtract 2x from both sides.
-\frac{1}{2}x-1>0
Combine \frac{3}{2}x and -2x to get -\frac{1}{2}x.
-\frac{1}{2}x>1
Add 1 to both sides. Anything plus zero gives itself.
x<1\left(-2\right)
Multiply both sides by -2, the reciprocal of -\frac{1}{2}. Since -\frac{1}{2} is negative, the inequality direction is changed.
x<-2
Multiply 1 and -2 to get -2.