Algebra Examples

$\frac{4}{5} (v - 7) = 2$

Step 1

Multiply both sides of the equation by $\frac{5}{4}$ .

$\frac{5}{4} (\frac{4}{5} \cdot (v - 7)) = \frac{5}{4} \cdot 2$

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 $\frac{5}{4} (\frac{4}{5} \cdot (v - 7))$ .

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Step 2.1.1.1

Apply the distributive property.

$\frac{5}{4} (\frac{4}{5} v + \frac{4}{5} \cdot - 7) = \frac{5}{4} \cdot 2$

Step 2.1.1.2

Combine $\frac{4}{5}$ and $v$ .

$\frac{5}{4} (\frac{4 v}{5} + \frac{4}{5} \cdot - 7) = \frac{5}{4} \cdot 2$

Step 2.1.1.3

Multiply $\frac{4}{5} \cdot - 7$ .

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Step 2.1.1.3.1

Combine $\frac{4}{5}$ and $- 7$ .

$\frac{5}{4} (\frac{4 v}{5} + \frac{4 \cdot - 7}{5}) = \frac{5}{4} \cdot 2$

Step 2.1.1.3.2

Multiply $4$ by $- 7$ .

$\frac{5}{4} (\frac{4 v}{5} + \frac{- 28}{5}) = \frac{5}{4} \cdot 2$

Step 2.1.1.4

Move the negative in front of the fraction.

$\frac{5}{4} (\frac{4 v}{5} - \frac{28}{5}) = \frac{5}{4} \cdot 2$

Step 2.1.1.5

Apply the distributive property.

$\frac{5}{4} \cdot \frac{4 v}{5} + \frac{5}{4} (- \frac{28}{5}) = \frac{5}{4} \cdot 2$

Step 2.1.1.6

Cancel the common factor of $5$ .

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Step 2.1.1.6.1

Cancel the common factor.

$\frac{5}{4} \cdot \frac{4 v}{5} + \frac{5}{4} (- \frac{28}{5}) = \frac{5}{4} \cdot 2$

Step 2.1.1.6.2

Rewrite the expression.

$\frac{1}{4} (4 v) + \frac{5}{4} (- \frac{28}{5}) = \frac{5}{4} \cdot 2$

Step 2.1.1.7

Cancel the common factor of $4$ .

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Step 2.1.1.7.1

Factor $4$ out of $4 v$ .

$\frac{1}{4} (4 (v)) + \frac{5}{4} (- \frac{28}{5}) = \frac{5}{4} \cdot 2$

Step 2.1.1.7.2

Cancel the common factor.

$\frac{1}{4} (4 v) + \frac{5}{4} (- \frac{28}{5}) = \frac{5}{4} \cdot 2$

Step 2.1.1.7.3

Rewrite the expression.

$v + \frac{5}{4} (- \frac{28}{5}) = \frac{5}{4} \cdot 2$

Step 2.1.1.8

Cancel the common factor of $5$ .

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Step 2.1.1.8.1

Move the leading negative in $- \frac{28}{5}$ into the numerator.

$v + \frac{5}{4} \cdot \frac{- 28}{5} = \frac{5}{4} \cdot 2$

Step 2.1.1.8.2

Cancel the common factor.

$v + \frac{5}{4} \cdot \frac{- 28}{5} = \frac{5}{4} \cdot 2$

Step 2.1.1.8.3

Rewrite the expression.

$v + \frac{1}{4} \cdot - 28 = \frac{5}{4} \cdot 2$

Step 2.1.1.9

Cancel the common factor of $4$ .

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Step 2.1.1.9.1

Factor $4$ out of $- 28$ .

$v + \frac{1}{4} \cdot (4 (- 7)) = \frac{5}{4} \cdot 2$

Step 2.1.1.9.2

Cancel the common factor.

$v + \frac{1}{4} \cdot (4 \cdot - 7) = \frac{5}{4} \cdot 2$

Step 2.1.1.9.3

Rewrite the expression.

$v - 7 = \frac{5}{4} \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Factor $2$ out of $4$ .

$v - 7 = \frac{5}{2 (2)} \cdot 2$

Step 2.2.1.2

Cancel the common factor.

$v - 7 = \frac{5}{2 \cdot 2} \cdot 2$

Step 2.2.1.3

Rewrite the expression.

$v - 7 = \frac{5}{2}$

Step 3

Move all terms not containing $v$ to the right side of the equation.

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Step 3.1

Add $7$ to both sides of the equation.

$v = \frac{5}{2} + 7$

Step 3.2

To write $7$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$v = \frac{5}{2} + 7 \cdot \frac{2}{2}$

Step 3.3

Combine $7$ and $\frac{2}{2}$ .

$v = \frac{5}{2} + \frac{7 \cdot 2}{2}$

Step 3.4

Combine the numerators over the common denominator.

$v = \frac{5 + 7 \cdot 2}{2}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $7$ by $2$ .

$v = \frac{5 + 14}{2}$

Step 3.5.2

Add $5$ and $14$ .

$v = \frac{19}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$v = \frac{19}{2}$

Decimal Form:

$v = 9.5$

Mixed Number Form:

$v = 9 \frac{1}{2}$