Solve 5-3/2x>1/3

$$5- \frac{ 3 }{ 2 } x > \frac{ 1 }{ 3 }$$

Solve for x

$$x<\frac{28}{9}$$

Solution Steps

Subtract 5 from both sides.

$$-\frac{3}{2}x>\frac{1}{3}-5$$

Convert 5 to fraction \frac{15}{3}.

$$-\frac{3}{2}x>\frac{1}{3}-\frac{15}{3}$$

Since \frac{1}{3} and \frac{15}{3} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{3}{2}x>\frac{1-15}{3}$$

Subtract 15 from 1 to get -14.

$$-\frac{3}{2}x>-\frac{14}{3}$$

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

$$x<-\frac{14}{3}\left(-\frac{2}{3}\right)$$

Multiply -\frac{14}{3} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$x<\frac{-14\left(-2\right)}{3\times 3}$$

Do the multiplications in the fraction \frac{-14\left(-2\right)}{3\times 3}.

$$x<\frac{28}{9}$$