How to solve (1)/(2xy)=z

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

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Question

$$\frac{ 1 }{ 2xy } =z$$

Solve for x

$x=\frac{1}{2yz}$
$z\neq 0\text{ and }y\neq 0$

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 $2xy$.

$$1=z\times 2xy$$

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

$$z\times 2xy=1$$

The equation is in standard form.

$$2yzx=1$$

Divide both sides by $2zy$.

$$\frac{2yzx}{2yz}=\frac{1}{2yz}$$

Dividing by $2zy$ undoes the multiplication by $2zy$.

$$x=\frac{1}{2yz}$$

Variable $x$ cannot be equal to $0$.

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

Show Solution

Solve for y

$y=\frac{1}{2xz}$
$z\neq 0\text{ and }x\neq 0$

Steps for Solving Linear Equation

Variable $y$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $2xy$.

$$1=z\times 2xy$$

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

$$z\times 2xy=1$$

The equation is in standard form.

$$2xzy=1$$

Divide both sides by $2zx$.

$$\frac{2xzy}{2xz}=\frac{1}{2xz}$$

Dividing by $2zx$ undoes the multiplication by $2zx$.

$$y=\frac{1}{2xz}$$

Variable $y$ cannot be equal to $0$.

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

Show Solution

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

Example

Question

Solve for x

Steps for Solving Linear Equation

Solve for y

Steps for Solving Linear Equation