Solve -3/2x+1/2>0

$$- \frac { 3 } { 2 } x + \frac { 1 } { 2 } > 0$$

Solve for x

$$x<\frac{1}{3}$$

Solution Steps

Subtract \frac{1}{2} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{3}{2}x>-\frac{1}{2}$$

Multiply both sides by -\frac{2}{3}, the reciprocal of -\frac{3}{2}. Since -\frac{3}{2} is negative, the inequality direction is changed.

$$x<-\frac{1}{2}\left(-\frac{2}{3}\right)$$

Multiply -\frac{1}{2} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$x<\frac{-\left(-2\right)}{2\times 3}$$

Do the multiplications in the fraction \frac{-\left(-2\right)}{2\times 3}.

$$x<\frac{2}{6}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$x<\frac{1}{3}$$