Solve y=frac{a_{1}}{2x}

$$y = \frac { a _ { 1 } } { 2 x }$$

Solve for a_1

$$a_{1}=2xy$$

$$x\neq 0$$

Solution Steps

Multiply both sides of the equation by 2x.

$$y\times 2x=a_{1}$$

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

$$a_{1}=y\times 2x$$

Solve for x

$$\left\{\begin{matrix}x=\frac{a_{1}}{2y}\text{, }&a_{1}\neq 0\text{ and }y\neq 0\\x\neq 0\text{, }&y=0\text{ and }a_{1}=0\end{matrix}\right.$$

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 2x.

$$y\times 2x=a_{1}$$

Reorder the terms.

$$2xy=a_{1}$$

The equation is in standard form.

$$2yx=a_{1}$$

Divide both sides by 2y.

$$\frac{2yx}{2y}=\frac{a_{1}}{2y}$$

Dividing by 2y undoes the multiplication by 2y.

$$x=\frac{a_{1}}{2y}$$

Variable x cannot be equal to 0.

$$x=\frac{a_{1}}{2y}\text{, }x\neq 0$$