Solve 4y/2ydivy+(-6w)-w+3y=x

$$\frac { 4 y } { 2 y } \div y + ( - 6 w ) - w + 3 y = x$$

Solve for w

$$w=\frac{3y}{7}-\frac{x}{7}+\frac{2}{7y}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y.

$$\frac{4y}{2y}-6wy-wy+3yy=xy$$

Multiply y and y to get y^{2}.

$$\frac{4y}{2y}-6wy-wy+3y^{2}=xy$$

Cancel out 2y in both numerator and denominator.

$$2-6wy-wy+3y^{2}=xy$$

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

$$2-7wy+3y^{2}=xy$$

Subtract 2 from both sides.

$$-7wy+3y^{2}=xy-2$$

Subtract 3y^{2} from both sides.

$$-7wy=xy-2-3y^{2}$$

The equation is in standard form.

$$\left(-7y\right)w=xy-3y^{2}-2$$

Divide both sides by -7y.

$$\frac{\left(-7y\right)w}{-7y}=\frac{xy-3y^{2}-2}{-7y}$$

Dividing by -7y undoes the multiplication by -7y.

$$w=\frac{xy-3y^{2}-2}{-7y}$$

Divide xy-2-3y^{2} by -7y.

$$w=\frac{3y}{7}-\frac{x}{7}+\frac{2}{7y}$$

Solve for x

$$x=3y-7w+\frac{2}{y}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y.

$$\frac{4y}{2y}-6wy-wy+3yy=xy$$

Multiply y and y to get y^{2}.

$$\frac{4y}{2y}-6wy-wy+3y^{2}=xy$$

Cancel out 2y in both numerator and denominator.

$$2-6wy-wy+3y^{2}=xy$$

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

$$2-7wy+3y^{2}=xy$$

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

$$xy=2-7wy+3y^{2}$$

The equation is in standard form.

$$yx=3y^{2}-7wy+2$$

Divide both sides by y.

$$\frac{yx}{y}=\frac{3y^{2}-7wy+2}{y}$$

Dividing by y undoes the multiplication by y.

$$x=\frac{3y^{2}-7wy+2}{y}$$

Divide 3y^{2}+2-7yw by y.

$$x=3y-7w+\frac{2}{y}$$