Basic Math Examples

$4 + 3 (2 v - 1) = - 3 (3 v - 2) + 5 v$

Step 1

Since $v$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- 3 (3 v - 2) + 5 v = 4 + 3 (2 v - 1)$

Step 2

Simplify $- 3 (3 v - 2) + 5 v$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$- 3 (3 v) - 3 \cdot - 2 + 5 v = 4 + 3 (2 v - 1)$

Step 2.1.2

Multiply $3$ by $- 3$ .

$- 9 v - 3 \cdot - 2 + 5 v = 4 + 3 (2 v - 1)$

Step 2.1.3

Multiply $- 3$ by $- 2$ .

$- 9 v + 6 + 5 v = 4 + 3 (2 v - 1)$

Step 2.2

Add $- 9 v$ and $5 v$ .

$- 4 v + 6 = 4 + 3 (2 v - 1)$

Step 3

Simplify $4 + 3 (2 v - 1)$ .

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Step 3.1

Simplify each term.

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Step 3.1.1

Apply the distributive property.

$- 4 v + 6 = 4 + 3 (2 v) + 3 \cdot - 1$

Step 3.1.2

Multiply $2$ by $3$ .

$- 4 v + 6 = 4 + 6 v + 3 \cdot - 1$

Step 3.1.3

Multiply $3$ by $- 1$ .

$- 4 v + 6 = 4 + 6 v - 3$

Step 3.2

Subtract $3$ from $4$ .

$- 4 v + 6 = 6 v + 1$

Step 4

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

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Step 4.1

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

$- 4 v + 6 - 6 v = 1$

Step 4.2

Subtract $6 v$ from $- 4 v$ .

$- 10 v + 6 = 1$

Step 5

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

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Step 5.1

Subtract $6$ from both sides of the equation.

$- 10 v = 1 - 6$

Step 5.2

Subtract $6$ from $1$ .

$- 10 v = - 5$

Step 6

Divide each term in $- 10 v = - 5$ by $- 10$ and simplify.

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Step 6.1

Divide each term in $- 10 v = - 5$ by $- 10$ .

$\frac{- 10 v}{- 10} = \frac{- 5}{- 10}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $- 10$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{- 10 v}{- 10} = \frac{- 5}{- 10}$

Step 6.2.1.2

Divide $v$ by $1$ .

$v = \frac{- 5}{- 10}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Cancel the common factor of $- 5$ and $- 10$ .

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Step 6.3.1.1

Factor $- 5$ out of $- 5$ .

$v = \frac{- 5 (1)}{- 10}$

Step 6.3.1.2

Cancel the common factors.

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Step 6.3.1.2.1

Factor $- 5$ out of $- 10$ .

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

Step 6.3.1.2.2

Cancel the common factor.

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

Step 6.3.1.2.3

Rewrite the expression.

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$v = 0.5$