Solve x/y+5=5/yz

$$\frac{ x }{ y } +5 = \frac{ 5 }{ y } z$$

Solve for x

$$x=5\left(z-y\right)$$

$$y\neq 0$$

Solution Steps

Multiply both sides of the equation by y.

$$x+y\times 5=5z$$

Subtract y\times 5 from both sides.

$$x=5z-y\times 5$$

Multiply -1 and 5 to get -5.

$$x=5z-5y$$

Solve for y

$$y=-\frac{x}{5}+z$$

$$x\neq 5z$$

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 y.

$$x+y\times 5=5z$$

Subtract x from both sides.

$$y\times 5=5z-x$$

The equation is in standard form.

$$5y=5z-x$$

Divide both sides by 5.

$$\frac{5y}{5}=\frac{5z-x}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$y=\frac{5z-x}{5}$$

Divide 5z-x by 5.

$$y=-\frac{x}{5}+z$$

Variable y cannot be equal to 0.

$$y=-\frac{x}{5}+z\text{, }y\neq 0$$