Algebra Examples

$x = \frac{7}{8} \cdot (y + z)$

Step 1

Rewrite the equation as $\frac{7}{8} \cdot (y + z) = x$ .

$\frac{7}{8} \cdot (y + z) = x$

Step 2

Multiply both sides of the equation by $\frac{8}{7}$ .

$\frac{8}{7} (\frac{7}{8} \cdot (y + z)) = \frac{8}{7} x$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{8}{7} (\frac{7}{8} \cdot (y + z))$ .

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Step 3.1.1.1

Apply the distributive property.

$\frac{8}{7} (\frac{7}{8} y + \frac{7}{8} z) = \frac{8}{7} x$

Step 3.1.1.2

Combine $\frac{7}{8}$ and $y$ .

$\frac{8}{7} (\frac{7 y}{8} + \frac{7}{8} z) = \frac{8}{7} x$

Step 3.1.1.3

Combine $\frac{7}{8}$ and $z$ .

$\frac{8}{7} (\frac{7 y}{8} + \frac{7 z}{8}) = \frac{8}{7} x$

Step 3.1.1.4

Apply the distributive property.

$\frac{8}{7} \cdot \frac{7 y}{8} + \frac{8}{7} \cdot \frac{7 z}{8} = \frac{8}{7} x$

Step 3.1.1.5

Cancel the common factor of $8$ .

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Step 3.1.1.5.1

Cancel the common factor.

$\frac{8}{7} \cdot \frac{7 y}{8} + \frac{8}{7} \cdot \frac{7 z}{8} = \frac{8}{7} x$

Step 3.1.1.5.2

Rewrite the expression.

$\frac{1}{7} (7 y) + \frac{8}{7} \cdot \frac{7 z}{8} = \frac{8}{7} x$

Step 3.1.1.6

Cancel the common factor of $7$ .

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Step 3.1.1.6.1

Factor $7$ out of $7 y$ .

$\frac{1}{7} (7 (y)) + \frac{8}{7} \cdot \frac{7 z}{8} = \frac{8}{7} x$

Step 3.1.1.6.2

Cancel the common factor.

$\frac{1}{7} (7 y) + \frac{8}{7} \cdot \frac{7 z}{8} = \frac{8}{7} x$

Step 3.1.1.6.3

Rewrite the expression.

$y + \frac{8}{7} \cdot \frac{7 z}{8} = \frac{8}{7} x$

Step 3.1.1.7

Cancel the common factor of $8$ .

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Step 3.1.1.7.1

Cancel the common factor.

$y + \frac{8}{7} \cdot \frac{7 z}{8} = \frac{8}{7} x$

Step 3.1.1.7.2

Rewrite the expression.

$y + \frac{1}{7} (7 z) = \frac{8}{7} x$

Step 3.1.1.8

Cancel the common factor of $7$ .

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Step 3.1.1.8.1

Factor $7$ out of $7 z$ .

$y + \frac{1}{7} (7 (z)) = \frac{8}{7} x$

Step 3.1.1.8.2

Cancel the common factor.

$y + \frac{1}{7} (7 z) = \frac{8}{7} x$

Step 3.1.1.8.3

Rewrite the expression.

$y + z = \frac{8}{7} x$

Step 3.2

Simplify the right side.

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Step 3.2.1

Combine $\frac{8}{7}$ and $x$ .

$y + z = \frac{8 x}{7}$

Step 4

Subtract $y$ from both sides of the equation.

$z = \frac{8 x}{7} - y$