Solve y-1/3-2=3y+1/2

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

Solve for y

$$y = -\frac{17}{7} = -2\frac{3}{7} \approx -2.428571429$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$2\left(y-1\right)-12=3\left(3y+1\right)$$

Use the distributive property to multiply 2 by y-1.

$$2y-2-12=3\left(3y+1\right)$$

Subtract 12 from -2 to get -14.

$$2y-14=3\left(3y+1\right)$$

Use the distributive property to multiply 3 by 3y+1.

$$2y-14=9y+3$$

Subtract 9y from both sides.

$$2y-14-9y=3$$

Combine 2y and -9y to get -7y.

$$-7y-14=3$$

Add 14 to both sides.

$$-7y=3+14$$

Add 3 and 14 to get 17.

$$-7y=17$$

Divide both sides by -7.

$$y=\frac{17}{-7}$$

Fraction \frac{17}{-7} can be rewritten as -\frac{17}{7} by extracting the negative sign.

$$y=-\frac{17}{7}$$