Solve 3y^-1=0.5x^4

$$3 y ^ { - 1 } = 0.5 x ^ { 4 }$$

Solve for y

$$y=\frac{6}{x^{4}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Reorder the terms.

$$3\times \frac{1}{y}=0.5x^{4}$$

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by y.

$$3\times 1=0.5x^{4}y$$

Multiply 3 and 1 to get 3.

$$3=0.5x^{4}y$$

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

$$0.5x^{4}y=3$$

The equation is in standard form.

$$\frac{x^{4}}{2}y=3$$

Divide both sides by 0.5x^{4}.

$$\frac{2\times \frac{x^{4}}{2}y}{x^{4}}=\frac{2\times 3}{x^{4}}$$

Dividing by 0.5x^{4} undoes the multiplication by 0.5x^{4}.

$$y=\frac{2\times 3}{x^{4}}$$

Divide 3 by 0.5x^{4}.

$$y=\frac{6}{x^{4}}$$

Variable y cannot be equal to 0.

$$y=\frac{6}{x^{4}}\text{, }y\neq 0$$

Solve for x (complex solution)

$$x=i\sqrt[4]{6}y^{-0.25}$$

$$x=\sqrt[4]{6}y^{-0.25}$$

$$x=-\sqrt[4]{6}y^{-0.25}$$

$$x=-i\sqrt[4]{6}y^{-0.25}\text{, }y\neq 0$$

Solve for x

$$x=\sqrt[4]{\frac{6}{y}}$$

$$x=-\sqrt[4]{\frac{6}{y}}\text{, }y>0$$