Solve 2y+1/3=31/2+2y

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

Solve for y

$$y = -\frac{19}{8} = -2\frac{3}{8} = -2.375$$

Steps for Solving Linear Equation

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

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

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

$$4y+2=3\left(3\times 2+1\right)+12y$$

Multiply 3 and 2 to get 6.

$$4y+2=3\left(6+1\right)+12y$$

Add 6 and 1 to get 7.

$$4y+2=3\times 7+12y$$

Multiply 3 and 7 to get 21.

$$4y+2=21+12y$$

Subtract 12y from both sides.

$$4y+2-12y=21$$

Combine 4y and -12y to get -8y.

$$-8y+2=21$$

Subtract 2 from both sides.

$$-8y=21-2$$

Subtract 2 from 21 to get 19.

$$-8y=19$$

Divide both sides by -8.

$$y=\frac{19}{-8}$$

Fraction \frac{19}{-8} can be rewritten as -\frac{19}{8} by extracting the negative sign.

$$y=-\frac{19}{8}$$