Solve y-9/8geqy+3/6

$$\frac{ y-9 }{ 8 } \geq \frac{ y+3 }{ 6 }$$

Solve for y

$$y\leq -39$$

Solution Steps

Multiply both sides of the equation by 24, the least common multiple of 8,6. Since 24 is positive, the inequality direction remains the same.

$$3\left(y-9\right)\geq 4\left(y+3\right)$$

Use the distributive property to multiply 3 by y-9.

$$3y-27\geq 4\left(y+3\right)$$

Use the distributive property to multiply 4 by y+3.

$$3y-27\geq 4y+12$$

Subtract 4y from both sides.

$$3y-27-4y\geq 12$$

Combine 3y and -4y to get -y.

$$-y-27\geq 12$$

Add 27 to both sides.

$$-y\geq 12+27$$

Add 12 and 27 to get 39.

$$-y\geq 39$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$y\leq -39$$