Solve 3y-13/12>5+2y/-6

$$\frac { 3 y - 13 } { 12 } > \frac { 5 + 2 y } { - 6 }$$

Solve for y

$$y>\frac{3}{7}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 12,-6. Since 12 is positive, the inequality direction remains the same.

$$3y-13>-2\left(5+2y\right)$$

Use the distributive property to multiply -2 by 5+2y.

$$3y-13>-10-4y$$

Add 4y to both sides.

$$3y-13+4y>-10$$

Combine 3y and 4y to get 7y.

$$7y-13>-10$$

Add 13 to both sides.

$$7y>-10+13$$

Add -10 and 13 to get 3.

$$7y>3$$

Divide both sides by 7. Since 7 is positive, the inequality direction remains the same.

$$y>\frac{3}{7}$$