Solve 4-3/2y<9/2-5/6y

$$4 - \frac { 3 } { 2 } y < \frac { 9 } { 2 } - \frac { 5 } { 6 } y$$

Solve for y

$$y>-\frac{3}{4}$$

Solution Steps

Add \frac{5}{6}y to both sides.

$$4-\frac{3}{2}y+\frac{5}{6}y<\frac{9}{2}$$

Combine -\frac{3}{2}y and \frac{5}{6}y to get -\frac{2}{3}y.

$$4-\frac{2}{3}y<\frac{9}{2}$$

Subtract 4 from both sides.

$$-\frac{2}{3}y<\frac{9}{2}-4$$

Convert 4 to fraction \frac{8}{2}.

$$-\frac{2}{3}y<\frac{9}{2}-\frac{8}{2}$$

Since \frac{9}{2} and \frac{8}{2} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{2}{3}y<\frac{9-8}{2}$$

Subtract 8 from 9 to get 1.

$$-\frac{2}{3}y<\frac{1}{2}$$

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

$$y>\frac{1}{2}\left(-\frac{3}{2}\right)$$

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

$$y>\frac{1\left(-3\right)}{2\times 2}$$

Do the multiplications in the fraction \frac{1\left(-3\right)}{2\times 2}.

$$y>\frac{-3}{4}$$

Fraction \frac{-3}{4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$y>-\frac{3}{4}$$