Solve 1+2y/18-1+4y/24=146y/6x

$$\frac { 1 + 2 y } { 18 } - \frac { 1 + 4 y } { 24 } = \frac { 146 y } { 6 x }$$

Solve for x

$$x=-\frac{1752y}{4y-1}$$

$$y\neq 0\text{ and }y\neq \frac{1}{4}$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 72x, the least common multiple of 18,24,6x.

$$4x\left(1+2y\right)-3x\left(1+4y\right)=12\times 146y$$

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

$$4x+8yx-3x\left(1+4y\right)=12\times 146y$$

Use the distributive property to multiply 3x by 1+4y.

$$4x+8yx-\left(3x+12yx\right)=12\times 146y$$

To find the opposite of 3x+12yx, find the opposite of each term.

$$4x+8yx-3x-12yx=12\times 146y$$

Combine 4x and -3x to get x.

$$x+8yx-12yx=12\times 146y$$

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

$$x-4yx=12\times 146y$$

Multiply 12 and 146 to get 1752.

$$x-4yx=1752y$$

Combine all terms containing x.

$$\left(1-4y\right)x=1752y$$

Divide both sides by 1-4y.

$$\frac{\left(1-4y\right)x}{1-4y}=\frac{1752y}{1-4y}$$

Dividing by 1-4y undoes the multiplication by 1-4y.

$$x=\frac{1752y}{1-4y}$$

Variable x cannot be equal to 0.

$$x=\frac{1752y}{1-4y}\text{, }x\neq 0$$

Solve for y

$$y=\frac{x}{4\left(x+438\right)}$$

$$x\neq -438\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 72x, the least common multiple of 18,24,6x.

$$4x\left(1+2y\right)-3x\left(1+4y\right)=12\times 146y$$

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

$$4x+8yx-3x\left(1+4y\right)=12\times 146y$$

Use the distributive property to multiply 3x by 1+4y.

$$4x+8yx-\left(3x+12yx\right)=12\times 146y$$

To find the opposite of 3x+12yx, find the opposite of each term.

$$4x+8yx-3x-12yx=12\times 146y$$

Combine 4x and -3x to get x.

$$x+8yx-12yx=12\times 146y$$

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

$$x-4yx=12\times 146y$$

Multiply 12 and 146 to get 1752.

$$x-4yx=1752y$$

Subtract 1752y from both sides.

$$x-4yx-1752y=0$$

Subtract x from both sides. Anything subtracted from zero gives its negation.

$$-4yx-1752y=-x$$

Combine all terms containing y.

$$\left(-4x-1752\right)y=-x$$

Divide both sides by -1752-4x.

$$\frac{\left(-4x-1752\right)y}{-4x-1752}=-\frac{x}{-4x-1752}$$

Dividing by -1752-4x undoes the multiplication by -1752-4x.

$$y=-\frac{x}{-4x-1752}$$

Divide -x by -1752-4x.

$$y=\frac{x}{4\left(x+438\right)}$$