Algebra Examples

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

Step 1

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

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

Step 2

Multiply both sides by $4$ .

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

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $4$ .

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Step 3.1.1.1

Cancel the common factor.

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

Step 3.1.1.2

Rewrite the expression.

$2 y - z = x \cdot 4$

Step 3.2

Simplify the right side.

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Step 3.2.1

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

$2 y - z = 4 x$

Step 4

Solve for $z$ .

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Step 4.1

Subtract $2 y$ from both sides of the equation.

$- z = 4 x - 2 y$

Step 4.2

Divide each term in $- z = 4 x - 2 y$ by $- 1$ and simplify.

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Step 4.2.1

Divide each term in $- z = 4 x - 2 y$ by $- 1$ .

$\frac{- z}{- 1} = \frac{4 x}{- 1} + \frac{- 2 y}{- 1}$

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.

$\frac{z}{1} = \frac{4 x}{- 1} + \frac{- 2 y}{- 1}$

Step 4.2.2.2

Divide $z$ by $1$ .

$z = \frac{4 x}{- 1} + \frac{- 2 y}{- 1}$

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 one from the denominator of $\frac{4 x}{- 1}$ .

$z = - 1 \cdot (4 x) + \frac{- 2 y}{- 1}$

Step 4.2.3.1.2

Rewrite $- 1 \cdot (4 x)$ as $- (4 x)$ .

$z = - (4 x) + \frac{- 2 y}{- 1}$

Step 4.2.3.1.3

Multiply $4$ by $- 1$ .

$z = - 4 x + \frac{- 2 y}{- 1}$

Step 4.2.3.1.4

Move the negative one from the denominator of $\frac{- 2 y}{- 1}$ .

$z = - 4 x - 1 \cdot (- 2 y)$

Step 4.2.3.1.5

Rewrite $- 1 \cdot (- 2 y)$ as $- (- 2 y)$ .

$z = - 4 x - (- 2 y)$

Step 4.2.3.1.6

Multiply $- 2$ by $- 1$ .

$z = - 4 x + 2 y$