Solve y-2/3-2y-3/6=y/9

$$\frac { y - 2 } { 3 } - \frac { 2 y - 3 } { 6 } = \frac { y } { 9 }$$

Solve for y

$$y = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 18, the least common multiple of 3,6,9.

$$6\left(y-2\right)-3\left(2y-3\right)=2y$$

Use the distributive property to multiply 6 by y-2.

$$6y-12-3\left(2y-3\right)=2y$$

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

$$6y-12-6y+9=2y$$

Combine 6y and -6y to get 0.

$$-12+9=2y$$

Add -12 and 9 to get -3.

$$-3=2y$$

Swap sides so that all variable terms are on the left hand side.

$$2y=-3$$

Divide both sides by 2.

$$y=\frac{-3}{2}$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$y=-\frac{3}{2}$$