Solve (y-12)/5+3y/4=(y+6)/2

$$\frac { ( y - 12 ) } { 5 } + \frac { 3 y } { 4 } = \frac { ( y + 6 ) } { 2 }$$

Solve for y

$$y=12$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 20, the least common multiple of 5,4,2.

$$4\left(y-12\right)+5\times 3y=10\left(y+6\right)$$

Use the distributive property to multiply 4 by y-12.

$$4y-48+5\times 3y=10\left(y+6\right)$$

Multiply 5 and 3 to get 15.

$$4y-48+15y=10\left(y+6\right)$$

Combine 4y and 15y to get 19y.

$$19y-48=10\left(y+6\right)$$

Use the distributive property to multiply 10 by y+6.

$$19y-48=10y+60$$

Subtract 10y from both sides.

$$19y-48-10y=60$$

Combine 19y and -10y to get 9y.

$$9y-48=60$$

Add 48 to both sides.

$$9y=60+48$$

Add 60 and 48 to get 108.

$$9y=108$$

Divide both sides by 9.

$$y=\frac{108}{9}$$

Divide 108 by 9 to get 12.

$$y=12$$