Algebra Examples

$3 (3 + 3 v) = - 2 (9 - 3 v)$

Step 1

Simplify $3 (3 + 3 v)$ .

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Step 1.1

Rewrite.

$0 + 0 + 3 (3 + 3 v) = - 2 (9 - 3 v)$

Step 1.2

Simplify by adding zeros.

$3 (3 + 3 v) = - 2 (9 - 3 v)$

Step 1.3

Apply the distributive property.

$3 \cdot 3 + 3 (3 v) = - 2 (9 - 3 v)$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $3$ by $3$ .

$9 + 3 (3 v) = - 2 (9 - 3 v)$

Step 1.4.2

Multiply $3$ by $3$ .

$9 + 9 v = - 2 (9 - 3 v)$

Step 2

Simplify $- 2 (9 - 3 v)$ .

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Step 2.1

Apply the distributive property.

$9 + 9 v = - 2 \cdot 9 - 2 (- 3 v)$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $- 2$ by $9$ .

$9 + 9 v = - 18 - 2 (- 3 v)$

Step 2.2.2

Multiply $- 3$ by $- 2$ .

$9 + 9 v = - 18 + 6 v$

Step 3

Move all terms containing $v$ to the left side of the equation.

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Step 3.1

Subtract $6 v$ from both sides of the equation.

$9 + 9 v - 6 v = - 18$

Step 3.2

Subtract $6 v$ from $9 v$ .

$9 + 3 v = - 18$

Step 4

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

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Step 4.1

Subtract $9$ from both sides of the equation.

$3 v = - 18 - 9$

Step 4.2

Subtract $9$ from $- 18$ .

$3 v = - 27$

Step 5

Divide each term in $3 v = - 27$ by $3$ and simplify.

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Step 5.1

Divide each term in $3 v = - 27$ by $3$ .

$\frac{3 v}{3} = \frac{- 27}{3}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $3$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{3 v}{3} = \frac{- 27}{3}$

Step 5.2.1.2

Divide $v$ by $1$ .

$v = \frac{- 27}{3}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $- 27$ by $3$ .

$v = - 9$