Solve 2x+1/3+x-5/4=1-3x+2/6y

$$\frac { 2 x + 1 } { 3 } + \frac { x - 5 } { 4 } = 1 - \frac { 3 x + 2 } { 6 } y$$

Solve for x

$$x=-\frac{4y-23}{6y+11}$$

$$y\neq -\frac{11}{6}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 3,4,6.

$$4\left(2x+1\right)+3\left(x-5\right)=12-2\left(3x+2\right)y$$

Use the distributive property to multiply 4 by 2x+1.

$$8x+4+3\left(x-5\right)=12-2\left(3x+2\right)y$$

Use the distributive property to multiply 3 by x-5.

$$8x+4+3x-15=12-2\left(3x+2\right)y$$

Combine 8x and 3x to get 11x.

$$11x+4-15=12-2\left(3x+2\right)y$$

Subtract 15 from 4 to get -11.

$$11x-11=12-2\left(3x+2\right)y$$

Add 2\left(3x+2\right)y to both sides.

$$11x-11+2\left(3x+2\right)y=12$$

Use the distributive property to multiply 2 by 3x+2.

$$11x-11+\left(6x+4\right)y=12$$

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

$$11x-11+6xy+4y=12$$

Add 11 to both sides.

$$11x+6xy+4y=12+11$$

Add 12 and 11 to get 23.

$$11x+6xy+4y=23$$

Subtract 4y from both sides.

$$11x+6xy=23-4y$$

Combine all terms containing x.

$$\left(11+6y\right)x=23-4y$$

The equation is in standard form.

$$\left(6y+11\right)x=23-4y$$

Divide both sides by 11+6y.

$$\frac{\left(6y+11\right)x}{6y+11}=\frac{23-4y}{6y+11}$$

Dividing by 11+6y undoes the multiplication by 11+6y.

$$x=\frac{23-4y}{6y+11}$$

Solve for y

$$y=\frac{23-11x}{2\left(3x+2\right)}$$

$$x\neq -\frac{2}{3}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 3,4,6.

$$4\left(2x+1\right)+3\left(x-5\right)=12-2\left(3x+2\right)y$$

Use the distributive property to multiply 4 by 2x+1.

$$8x+4+3\left(x-5\right)=12-2\left(3x+2\right)y$$

Use the distributive property to multiply 3 by x-5.

$$8x+4+3x-15=12-2\left(3x+2\right)y$$

Combine 8x and 3x to get 11x.

$$11x+4-15=12-2\left(3x+2\right)y$$

Subtract 15 from 4 to get -11.

$$11x-11=12-2\left(3x+2\right)y$$

Swap sides so that all variable terms are on the left hand side.

$$12-2\left(3x+2\right)y=11x-11$$

Use the distributive property to multiply -2 by 3x+2.

$$12+\left(-6x-4\right)y=11x-11$$

Use the distributive property to multiply -6x-4 by y.

$$12-6xy-4y=11x-11$$

Subtract 12 from both sides.

$$-6xy-4y=11x-11-12$$

Subtract 12 from -11 to get -23.

$$-6xy-4y=11x-23$$

Combine all terms containing y.

$$\left(-6x-4\right)y=11x-23$$

Divide both sides by -6x-4.

$$\frac{\left(-6x-4\right)y}{-6x-4}=\frac{11x-23}{-6x-4}$$

Dividing by -6x-4 undoes the multiplication by -6x-4.

$$y=\frac{11x-23}{-6x-4}$$

Divide 11x-23 by -6x-4.

$$y=-\frac{11x-23}{2\left(3x+2\right)}$$