Solve 3y+2/4-y-6/3>0

$$\frac { 3 y + 2 } { 4 } - \frac { y - 6 } { 3 } > 0$$

Solve for y

$$y>-6$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 4,3. Since 12 is positive, the inequality direction remains the same.

$$3\left(3y+2\right)-4\left(y-6\right)>0$$

Use the distributive property to multiply 3 by 3y+2.

$$9y+6-4\left(y-6\right)>0$$

Use the distributive property to multiply -4 by y-6.

$$9y+6-4y+24>0$$

Combine 9y and -4y to get 5y.

$$5y+6+24>0$$

Add 6 and 24 to get 30.

$$5y+30>0$$

Subtract 30 from both sides. Anything subtracted from zero gives its negation.

$$5y>-30$$

Divide both sides by 5. Since 5 is positive, the inequality direction remains the same.

$$y>\frac{-30}{5}$$

Divide -30 by 5 to get -6.

$$y>-6$$