Algebra Examples

$(v + 5) (- \frac{1}{9}) = 6$

Step 1

Multiply each term in $(v + 5) (- \frac{1}{9}) = 6$ by $- 9$ to eliminate the fractions.

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Step 1.1

Multiply each term in $(v + 5) (- \frac{1}{9}) = 6$ by $- 9$ .

$(v + 5) (- \frac{1}{9}) \cdot - 9 = 6 \cdot - 9$

Step 1.2

Simplify the left side.

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Step 1.2.1

Apply the distributive property.

$(v (- \frac{1}{9}) + 5 (- \frac{1}{9})) \cdot - 9 = 6 \cdot - 9$

Step 1.2.2

Combine $v$ and $\frac{1}{9}$ .

$(- \frac{v}{9} + 5 (- \frac{1}{9})) \cdot - 9 = 6 \cdot - 9$

Step 1.2.3

Multiply $5 (- \frac{1}{9})$ .

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Step 1.2.3.1

Multiply $- 1$ by $5$ .

$(- \frac{v}{9} - 5 (\frac{1}{9})) \cdot - 9 = 6 \cdot - 9$

Step 1.2.3.2

Combine $- 5$ and $\frac{1}{9}$ .

$(- \frac{v}{9} + \frac{- 5}{9}) \cdot - 9 = 6 \cdot - 9$

Step 1.2.4

Move the negative in front of the fraction.

$(- \frac{v}{9} - \frac{5}{9}) \cdot - 9 = 6 \cdot - 9$

Step 1.2.5

Apply the distributive property.

$- \frac{v}{9} \cdot - 9 - \frac{5}{9} \cdot - 9 = 6 \cdot - 9$

Step 1.2.6

Cancel the common factor of $9$ .

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Step 1.2.6.1

Move the leading negative in $- \frac{v}{9}$ into the numerator.

$\frac{- v}{9} \cdot - 9 - \frac{5}{9} \cdot - 9 = 6 \cdot - 9$

Step 1.2.6.2

Factor $9$ out of $- 9$ .

$\frac{- v}{9} \cdot (9 (- 1)) - \frac{5}{9} \cdot - 9 = 6 \cdot - 9$

Step 1.2.6.3

Cancel the common factor.

$\frac{- v}{9} \cdot (9 \cdot - 1) - \frac{5}{9} \cdot - 9 = 6 \cdot - 9$

Step 1.2.6.4

Rewrite the expression.

$- v \cdot - 1 - \frac{5}{9} \cdot - 9 = 6 \cdot - 9$

Step 1.2.7

Multiply.

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Step 1.2.7.1

Multiply $- 1$ by $- 1$ .

$1 v - \frac{5}{9} \cdot - 9 = 6 \cdot - 9$

Step 1.2.7.2

Multiply $v$ by $1$ .

$v - \frac{5}{9} \cdot - 9 = 6 \cdot - 9$

Step 1.2.8

Cancel the common factor of $9$ .

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Step 1.2.8.1

Move the leading negative in $- \frac{5}{9}$ into the numerator.

$v + \frac{- 5}{9} \cdot - 9 = 6 \cdot - 9$

Step 1.2.8.2

Factor $9$ out of $- 9$ .

$v + \frac{- 5}{9} \cdot (9 (- 1)) = 6 \cdot - 9$

Step 1.2.8.3

Cancel the common factor.

$v + \frac{- 5}{9} \cdot (9 \cdot - 1) = 6 \cdot - 9$

Step 1.2.8.4

Rewrite the expression.

$v - 5 \cdot - 1 = 6 \cdot - 9$

Step 1.2.9

Multiply $- 5$ by $- 1$ .

$v + 5 = 6 \cdot - 9$

Step 1.3

Simplify the right side.

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Step 1.3.1

Multiply $6$ by $- 9$ .

$v + 5 = - 54$

Step 2

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

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Step 2.1

Subtract $5$ from both sides of the equation.

$v = - 54 - 5$

Step 2.2

Subtract $5$ from $- 54$ .

$v = - 59$