Algebra Examples

$D = \frac{7}{8} (f - g)$

Step 1

Rewrite the equation as $\frac{7}{8} \cdot (f - g) = D$ .

$\frac{7}{8} \cdot (f - g) = D$

Step 2

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

$\frac{8}{7} (\frac{7}{8} \cdot (f - g)) = \frac{8}{7} D$

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 $\frac{8}{7} (\frac{7}{8} \cdot (f - g))$ .

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Step 3.1.1.1

Apply the distributive property.

$\frac{8}{7} (\frac{7}{8} f + \frac{7}{8} (- g)) = \frac{8}{7} D$

Step 3.1.1.2

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

$\frac{8}{7} (\frac{7 f}{8} + \frac{7}{8} (- g)) = \frac{8}{7} D$

Step 3.1.1.3

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

$\frac{8}{7} (\frac{7 f}{8} - \frac{7 g}{8}) = \frac{8}{7} D$

Step 3.1.1.4

Apply the distributive property.

$\frac{8}{7} \cdot \frac{7 f}{8} + \frac{8}{7} (- \frac{7 g}{8}) = \frac{8}{7} D$

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.

$\frac{8}{7} \cdot \frac{7 f}{8} + \frac{8}{7} (- \frac{7 g}{8}) = \frac{8}{7} D$

Step 3.1.1.5.2

Rewrite the expression.

$\frac{1}{7} (7 f) + \frac{8}{7} (- \frac{7 g}{8}) = \frac{8}{7} D$

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 $7 f$ .

$\frac{1}{7} (7 (f)) + \frac{8}{7} (- \frac{7 g}{8}) = \frac{8}{7} D$

Step 3.1.1.6.2

Cancel the common factor.

$\frac{1}{7} (7 f) + \frac{8}{7} (- \frac{7 g}{8}) = \frac{8}{7} D$

Step 3.1.1.6.3

Rewrite the expression.

$f + \frac{8}{7} (- \frac{7 g}{8}) = \frac{8}{7} D$

Step 3.1.1.7

Cancel the common factor of $8$ .

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Step 3.1.1.7.1

Move the leading negative in $- \frac{7 g}{8}$ into the numerator.

$f + \frac{8}{7} \cdot \frac{- 7 g}{8} = \frac{8}{7} D$

Step 3.1.1.7.2

Cancel the common factor.

$f + \frac{8}{7} \cdot \frac{- 7 g}{8} = \frac{8}{7} D$

Step 3.1.1.7.3

Rewrite the expression.

$f + \frac{1}{7} (- 7 g) = \frac{8}{7} D$

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 $- 7 g$ .

$f + \frac{1}{7} (7 (- g)) = \frac{8}{7} D$

Step 3.1.1.8.2

Cancel the common factor.

$f + \frac{1}{7} (7 (- g)) = \frac{8}{7} D$

Step 3.1.1.8.3

Rewrite the expression.

$f - g = \frac{8}{7} D$

Step 3.2

Simplify the right side.

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Step 3.2.1

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

$f - g = \frac{8 D}{7}$

Step 4

Subtract $f$ from both sides of the equation.

$- g = \frac{8 D}{7} - f$

Step 5

Divide each term in $- g = \frac{8 D}{7} - f$ by $- 1$ and simplify.

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Step 5.1

Divide each term in $- g = \frac{8 D}{7} - f$ by $- 1$ .

$\frac{- g}{- 1} = \frac{\frac{8 D}{7}}{- 1} + \frac{- f}{- 1}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Dividing two negative values results in a positive value.

$\frac{g}{1} = \frac{\frac{8 D}{7}}{- 1} + \frac{- f}{- 1}$

Step 5.2.2

Divide $g$ by $1$ .

$g = \frac{\frac{8 D}{7}}{- 1} + \frac{- f}{- 1}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Simplify each term.

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Step 5.3.1.1

Move the negative one from the denominator of $\frac{\frac{8 D}{7}}{- 1}$ .

$g = - 1 \cdot \frac{8 D}{7} + \frac{- f}{- 1}$

Step 5.3.1.2

Rewrite $- 1 \cdot \frac{8 D}{7}$ as $- \frac{8 D}{7}$ .

$g = - \frac{8 D}{7} + \frac{- f}{- 1}$

Step 5.3.1.3

Dividing two negative values results in a positive value.

$g = - \frac{8 D}{7} + \frac{f}{1}$

Step 5.3.1.4

Divide $f$ by $1$ .

$g = - \frac{8 D}{7} + f$