Finite Math Examples

$4 x - \frac{5}{y} = 2 z$

Step 1

Rewrite the equation as $2 z = 4 x - \frac{5}{y}$ .

$2 z = 4 x - \frac{5}{y}$

Step 2

Divide each term in $2 z = 4 x - \frac{5}{y}$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 z = 4 x - \frac{5}{y}$ by $2$ .

$\frac{2 z}{2} = \frac{4 x}{2} + \frac{- \frac{5}{y}}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 z}{2} = \frac{4 x}{2} + \frac{- \frac{5}{y}}{2}$

Step 2.2.1.2

Divide $z$ by $1$ .

$z = \frac{4 x}{2} + \frac{- \frac{5}{y}}{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Cancel the common factor of $4$ and $2$ .

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Step 2.3.1.1.1

Factor $2$ out of $4 x$ .

$z = \frac{2 (2 x)}{2} + \frac{- \frac{5}{y}}{2}$

Step 2.3.1.1.2

Cancel the common factors.

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Step 2.3.1.1.2.1

Factor $2$ out of $2$ .

$z = \frac{2 (2 x)}{2 (1)} + \frac{- \frac{5}{y}}{2}$

Step 2.3.1.1.2.2

Cancel the common factor.

$z = \frac{2 (2 x)}{2 \cdot 1} + \frac{- \frac{5}{y}}{2}$

Step 2.3.1.1.2.3

Rewrite the expression.

$z = \frac{2 x}{1} + \frac{- \frac{5}{y}}{2}$

Step 2.3.1.1.2.4

Divide $2 x$ by $1$ .

$z = 2 x + \frac{- \frac{5}{y}}{2}$

Step 2.3.1.2

Multiply the numerator by the reciprocal of the denominator.

$z = 2 x - \frac{5}{y} \cdot \frac{1}{2}$

Step 2.3.1.3

Multiply $\frac{1}{2}$ by $\frac{5}{y}$ .

$z = 2 x - \frac{5}{2 y}$