Solve 2x+3+(y-1)4x-1=30x-4

$$2x+3+(y-1)4x-1=30x-4$$

Solve for x

$$x=-\frac{3}{2\left(y-8\right)}$$

$$y\neq 8$$

Steps for Solving Linear Equation

Use the distributive property to multiply y-1 by 4.

$$2x+3+\left(4y-4\right)x-1=30x-4$$

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

$$2x+3+4yx-4x-1=30x-4$$

Combine 2x and -4x to get -2x.

$$-2x+3+4yx-1=30x-4$$

Subtract 1 from 3 to get 2.

$$-2x+2+4yx=30x-4$$

Subtract 30x from both sides.

$$-2x+2+4yx-30x=-4$$

Combine -2x and -30x to get -32x.

$$-32x+2+4yx=-4$$

Subtract 2 from both sides.

$$-32x+4yx=-4-2$$

Subtract 2 from -4 to get -6.

$$-32x+4yx=-6$$

Combine all terms containing x.

$$\left(-32+4y\right)x=-6$$

The equation is in standard form.

$$\left(4y-32\right)x=-6$$

Divide both sides by 4y-32.

$$\frac{\left(4y-32\right)x}{4y-32}=-\frac{6}{4y-32}$$

Dividing by 4y-32 undoes the multiplication by 4y-32.

$$x=-\frac{6}{4y-32}$$

Divide -6 by 4y-32.

$$x=-\frac{3}{2\left(y-8\right)}$$

Solve for y

$$y=8-\frac{3}{2x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply y-1 by 4.

$$2x+3+\left(4y-4\right)x-1=30x-4$$

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

$$2x+3+4yx-4x-1=30x-4$$

Combine 2x and -4x to get -2x.

$$-2x+3+4yx-1=30x-4$$

Subtract 1 from 3 to get 2.

$$-2x+2+4yx=30x-4$$

Add 2x to both sides.

$$2+4yx=30x-4+2x$$

Combine 30x and 2x to get 32x.

$$2+4yx=32x-4$$

Subtract 2 from both sides.

$$4yx=32x-4-2$$

Subtract 2 from -4 to get -6.

$$4yx=32x-6$$

The equation is in standard form.

$$4xy=32x-6$$

Divide both sides by 4x.

$$\frac{4xy}{4x}=\frac{32x-6}{4x}$$

Dividing by 4x undoes the multiplication by 4x.

$$y=\frac{32x-6}{4x}$$

Divide 32x-6 by 4x.

$$y=8-\frac{3}{2x}$$