Solve 6-y/4-3=2y+6/7-y+4/2

$$\frac { 6 - y } { 4 } - 3 = \frac { 2 y + 6 } { 7 } - \frac { y + 4 } { 2 }$$

Solve for y

$$y=-10$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 28, the least common multiple of 4,7,2.

$$7\left(6-y\right)-84=4\left(2y+6\right)-14\left(y+4\right)$$

Use the distributive property to multiply 7 by 6-y.

$$42-7y-84=4\left(2y+6\right)-14\left(y+4\right)$$

Subtract 84 from 42 to get -42.

$$-42-7y=4\left(2y+6\right)-14\left(y+4\right)$$

Use the distributive property to multiply 4 by 2y+6.

$$-42-7y=8y+24-14\left(y+4\right)$$

Use the distributive property to multiply -14 by y+4.

$$-42-7y=8y+24-14y-56$$

Combine 8y and -14y to get -6y.

$$-42-7y=-6y+24-56$$

Subtract 56 from 24 to get -32.

$$-42-7y=-6y-32$$

Add 6y to both sides.

$$-42-7y+6y=-32$$

Combine -7y and 6y to get -y.

$$-42-y=-32$$

Add 42 to both sides.

$$-y=-32+42$$

Add -32 and 42 to get 10.

$$-y=10$$

Multiply both sides by -1.

$$y=-10$$