Solve 3y+1/16+2y-3/7=y+3/8+3y-1/14

$$\frac { 3 y + 1 } { 16 } + \frac { 2 y - 3 } { 7 } = \frac { y + 3 } { 8 } + \frac { 3 y - 1 } { 14 }$$

Solve for y

$$y=5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 112, the least common multiple of 16,7,8,14.

$$7\left(3y+1\right)+16\left(2y-3\right)=14\left(y+3\right)+8\left(3y-1\right)$$

Use the distributive property to multiply 7 by 3y+1.

$$21y+7+16\left(2y-3\right)=14\left(y+3\right)+8\left(3y-1\right)$$

Use the distributive property to multiply 16 by 2y-3.

$$21y+7+32y-48=14\left(y+3\right)+8\left(3y-1\right)$$

Combine 21y and 32y to get 53y.

$$53y+7-48=14\left(y+3\right)+8\left(3y-1\right)$$

Subtract 48 from 7 to get -41.

$$53y-41=14\left(y+3\right)+8\left(3y-1\right)$$

Use the distributive property to multiply 14 by y+3.

$$53y-41=14y+42+8\left(3y-1\right)$$

Use the distributive property to multiply 8 by 3y-1.

$$53y-41=14y+42+24y-8$$

Combine 14y and 24y to get 38y.

$$53y-41=38y+42-8$$

Subtract 8 from 42 to get 34.

$$53y-41=38y+34$$

Subtract 38y from both sides.

$$53y-41-38y=34$$

Combine 53y and -38y to get 15y.

$$15y-41=34$$

Add 41 to both sides.

$$15y=34+41$$

Add 34 and 41 to get 75.

$$15y=75$$

Divide both sides by 15.

$$y=\frac{75}{15}$$

Divide 75 by 15 to get 5.

$$y=5$$