Basic Math Examples

$\frac{2 \cdot - 1}{y} = \frac{w + 2}{2 z}$

Step 1

Rewrite the equation as $\frac{w + 2}{2 z} = \frac{2 \cdot - 1}{y}$ .

$\frac{w + 2}{2 z} = \frac{2 \cdot - 1}{y}$

Step 2

Multiply both sides by $2 z$ .

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

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{w + 2}{2 z} (2 z)$ .

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Step 3.1.1.1

Rewrite using the commutative property of multiplication.

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

Step 3.1.1.2

Cancel the common factor of $2$ .

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Step 3.1.1.2.1

Factor $2$ out of $2 z$ .

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

Step 3.1.1.2.2

Cancel the common factor.

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

Step 3.1.1.2.3

Rewrite the expression.

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

Step 3.1.1.3

Cancel the common factor of $z$ .

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Step 3.1.1.3.1

Cancel the common factor.

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

Step 3.1.1.3.2

Rewrite the expression.

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

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{2 \cdot - 1}{y} (2 z)$ .

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Step 3.2.1.1

Rewrite using the commutative property of multiplication.

$w + 2 = 2 \frac{2 \cdot - 1}{y} z$

Step 3.2.1.2

Multiply $2$ by $- 1$ .

$w + 2 = 2 \frac{- 2}{y} z$

Step 3.2.1.3

Move the negative in front of the fraction.

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

Step 3.2.1.4

Multiply $2 (- \frac{2}{y})$ .

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Step 3.2.1.4.1

Multiply $- 1$ by $2$ .

$w + 2 = - 2 \frac{2}{y} z$

Step 3.2.1.4.2

Combine $- 2$ and $\frac{2}{y}$ .

$w + 2 = \frac{- 2 \cdot 2}{y} z$

Step 3.2.1.4.3

Multiply $- 2$ by $2$ .

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

Step 3.2.1.5

Move the negative in front of the fraction.

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

Step 3.2.1.6

Combine $z$ and $\frac{4}{y}$ .

$w + 2 = - \frac{z \cdot 4}{y}$

Step 3.2.1.7

Move $4$ to the left of $z$ .

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

Step 4

Subtract $2$ from both sides of the equation.

$w = - \frac{4 z}{y} - 2$