Algebra Examples

$\frac{3}{4} (y - z) = x$

Step 1

Multiply both sides of the equation by $\frac{4}{3}$ .

$\frac{4}{3} (\frac{3}{4} \cdot (y - z)) = \frac{4}{3} x$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{4}{3} (\frac{3}{4} \cdot (y - z))$ .

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Step 2.1.1.1

Apply the distributive property.

$\frac{4}{3} (\frac{3}{4} y + \frac{3}{4} (- z)) = \frac{4}{3} x$

Step 2.1.1.2

Combine $\frac{3}{4}$ and $y$ .

$\frac{4}{3} (\frac{3 y}{4} + \frac{3}{4} (- z)) = \frac{4}{3} x$

Step 2.1.1.3

Combine $\frac{3}{4}$ and $z$ .

$\frac{4}{3} (\frac{3 y}{4} - \frac{3 z}{4}) = \frac{4}{3} x$

Step 2.1.1.4

Apply the distributive property.

$\frac{4}{3} \cdot \frac{3 y}{4} + \frac{4}{3} (- \frac{3 z}{4}) = \frac{4}{3} x$

Step 2.1.1.5

Cancel the common factor of $4$ .

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Step 2.1.1.5.1

Cancel the common factor.

$\frac{4}{3} \cdot \frac{3 y}{4} + \frac{4}{3} (- \frac{3 z}{4}) = \frac{4}{3} x$

Step 2.1.1.5.2

Rewrite the expression.

$\frac{1}{3} (3 y) + \frac{4}{3} (- \frac{3 z}{4}) = \frac{4}{3} x$

Step 2.1.1.6

Cancel the common factor of $3$ .

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Step 2.1.1.6.1

Factor $3$ out of $3 y$ .

$\frac{1}{3} (3 (y)) + \frac{4}{3} (- \frac{3 z}{4}) = \frac{4}{3} x$

Step 2.1.1.6.2

Cancel the common factor.

$\frac{1}{3} (3 y) + \frac{4}{3} (- \frac{3 z}{4}) = \frac{4}{3} x$

Step 2.1.1.6.3

Rewrite the expression.

$y + \frac{4}{3} (- \frac{3 z}{4}) = \frac{4}{3} x$

Step 2.1.1.7

Cancel the common factor of $4$ .

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Step 2.1.1.7.1

Move the leading negative in $- \frac{3 z}{4}$ into the numerator.

$y + \frac{4}{3} \cdot \frac{- 3 z}{4} = \frac{4}{3} x$

Step 2.1.1.7.2

Cancel the common factor.

$y + \frac{4}{3} \cdot \frac{- 3 z}{4} = \frac{4}{3} x$

Step 2.1.1.7.3

Rewrite the expression.

$y + \frac{1}{3} (- 3 z) = \frac{4}{3} x$

Step 2.1.1.8

Cancel the common factor of $3$ .

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Step 2.1.1.8.1

Factor $3$ out of $- 3 z$ .

$y + \frac{1}{3} (3 (- z)) = \frac{4}{3} x$

Step 2.1.1.8.2

Cancel the common factor.

$y + \frac{1}{3} (3 (- z)) = \frac{4}{3} x$

Step 2.1.1.8.3

Rewrite the expression.

$y - z = \frac{4}{3} x$

Step 2.2

Simplify the right side.

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Step 2.2.1

Combine $\frac{4}{3}$ and $x$ .

$y - z = \frac{4 x}{3}$

Step 3

Subtract $y$ from both sides of the equation.

$- z = \frac{4 x}{3} - y$

Step 4

Divide each term in $- z = \frac{4 x}{3} - y$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- z = \frac{4 x}{3} - y$ by $- 1$ .

$\frac{- z}{- 1} = \frac{\frac{4 x}{3}}{- 1} + \frac{- y}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{z}{1} = \frac{\frac{4 x}{3}}{- 1} + \frac{- y}{- 1}$

Step 4.2.2

Divide $z$ by $1$ .

$z = \frac{\frac{4 x}{3}}{- 1} + \frac{- y}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Move the negative one from the denominator of $\frac{\frac{4 x}{3}}{- 1}$ .

$z = - 1 \cdot \frac{4 x}{3} + \frac{- y}{- 1}$

Step 4.3.1.2

Rewrite $- 1 \cdot \frac{4 x}{3}$ as $- \frac{4 x}{3}$ .

$z = - \frac{4 x}{3} + \frac{- y}{- 1}$

Step 4.3.1.3

Dividing two negative values results in a positive value.

$z = - \frac{4 x}{3} + \frac{y}{1}$

Step 4.3.1.4

Divide $y$ by $1$ .

$z = - \frac{4 x}{3} + y$