Precalculus Examples

$x = \frac{w (6 - v)}{z}$

Step 1

Rewrite the equation as $\frac{w (6 - v)}{z} = x$ .

$\frac{w (6 - v)}{z} = x$

Step 2

Multiply both sides by $z$ .

$\frac{w (6 - v)}{z} z = x z$

Step 3

Simplify the left side.

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Step 3.1

Simplify $\frac{w (6 - v)}{z} z$ .

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Step 3.1.1

Cancel the common factor of $z$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{w (6 - v)}{z} z = x z$

Step 3.1.1.2

Rewrite the expression.

$w (6 - v) = x z$

Step 3.1.2

Apply the distributive property.

$w \cdot 6 + w (- v) = x z$

Step 3.1.3

Simplify the expression.

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Step 3.1.3.1

Move $6$ to the left of $w$ .

$6 \cdot w + w (- v) = x z$

Step 3.1.3.2

Rewrite using the commutative property of multiplication.

$6 \cdot w - w v = x z$

Step 3.1.3.3

Move $w$ .

$6 w - v w = x z$

Step 3.1.3.4

Reorder $6 w$ and $- v w$ .

$- v w + 6 w = x z$

Step 4

Solve for $v$ .

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Step 4.1

Subtract $6 w$ from both sides of the equation.

$- v w = x z - 6 w$

Step 4.2

Divide each term in $- v w = x z - 6 w$ by $- w$ and simplify.

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Step 4.2.1

Divide each term in $- v w = x z - 6 w$ by $- w$ .

$\frac{- v w}{- w} = \frac{x z}{- w} + \frac{- 6 w}{- w}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Dividing two negative values results in a positive value.

$\frac{v w}{w} = \frac{x z}{- w} + \frac{- 6 w}{- w}$

Step 4.2.2.2

Cancel the common factor of $w$ .

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Step 4.2.2.2.1

Cancel the common factor.

$\frac{v w}{w} = \frac{x z}{- w} + \frac{- 6 w}{- w}$

Step 4.2.2.2.2

Divide $v$ by $1$ .

$v = \frac{x z}{- w} + \frac{- 6 w}{- w}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Simplify each term.

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Step 4.2.3.1.1

Move the negative in front of the fraction.

$v = - \frac{x z}{w} + \frac{- 6 w}{- w}$

Step 4.2.3.1.2

Cancel the common factor of $w$ .

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Step 4.2.3.1.2.1

Cancel the common factor.

$v = - \frac{x z}{w} + \frac{- 6 w}{- w}$

Step 4.2.3.1.2.2

Rewrite the expression.

$v = - \frac{x z}{w} + \frac{- 6}{- 1}$

Step 4.2.3.1.2.3

Move the negative one from the denominator of $\frac{- 6}{- 1}$ .

$v = - \frac{x z}{w} - 1 \cdot - 6$

Step 4.2.3.1.3

Rewrite $- 1 \cdot - 6$ as $- - 6$ .

$v = - \frac{x z}{w} - - 6$

Step 4.2.3.1.4

Multiply $- 1$ by $- 6$ .

$v = - \frac{x z}{w} + 6$