Solve 9-2y(3k-5/2)=k

$$9 - 2 y ( \frac { 3 k - 5 } { 2 } ) = k$$

Solve for k

$$k=\frac{5y+9}{3y+1}$$

$$y\neq -\frac{1}{3}$$

Steps for Solving Linear Equation

Express 2\times \frac{3k-5}{2} as a single fraction.

$$9-\frac{2\left(3k-5\right)}{2}y=k$$

Cancel out 2 and 2.

$$9-\left(3k-5\right)y=k$$

Use the distributive property to multiply 3k-5 by y.

$$9-\left(3ky-5y\right)=k$$

To find the opposite of 3ky-5y, find the opposite of each term.

$$9-3ky+5y=k$$

Subtract k from both sides.

$$9-3ky+5y-k=0$$

Subtract 9 from both sides. Anything subtracted from zero gives its negation.

$$-3ky+5y-k=-9$$

Subtract 5y from both sides.

$$-3ky-k=-9-5y$$

Combine all terms containing k.

$$\left(-3y-1\right)k=-9-5y$$

The equation is in standard form.

$$\left(-3y-1\right)k=-5y-9$$

Divide both sides by -3y-1.

$$\frac{\left(-3y-1\right)k}{-3y-1}=\frac{-5y-9}{-3y-1}$$

Dividing by -3y-1 undoes the multiplication by -3y-1.

$$k=\frac{-5y-9}{-3y-1}$$

Divide -9-5y by -3y-1.

$$k=\frac{5y+9}{3y+1}$$

Solve for y

$$y=-\frac{9-k}{5-3k}$$

$$k\neq \frac{5}{3}$$

Steps for Solving Linear Equation

Express 2\times \frac{3k-5}{2} as a single fraction.

$$9-\frac{2\left(3k-5\right)}{2}y=k$$

Cancel out 2 and 2.

$$9-\left(3k-5\right)y=k$$

Use the distributive property to multiply 3k-5 by y.

$$9-\left(3ky-5y\right)=k$$

To find the opposite of 3ky-5y, find the opposite of each term.

$$9-3ky+5y=k$$

Subtract 9 from both sides.

$$-3ky+5y=k-9$$

Combine all terms containing y.

$$\left(-3k+5\right)y=k-9$$

The equation is in standard form.

$$\left(5-3k\right)y=k-9$$

Divide both sides by 5-3k.

$$\frac{\left(5-3k\right)y}{5-3k}=\frac{k-9}{5-3k}$$

Dividing by 5-3k undoes the multiplication by 5-3k.

$$y=\frac{k-9}{5-3k}$$