Algebra Examples

$- 2 v - 5 = 7 + 3 v - 3 v$

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.

$7 + 3 v - 3 v = - 2 v - 5$

Step 2

Combine the opposite terms in $7 + 3 v - 3 v$ .

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Step 2.1

Subtract $3 v$ from $3 v$ .

$7 + 0 = - 2 v - 5$

Step 2.2

Add $7$ and $0$ .

$7 = - 2 v - 5$

Step 3

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

$- 2 v - 5 = 7$

Step 4

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

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Step 4.1

Add $5$ to both sides of the equation.

$- 2 v = 7 + 5$

Step 4.2

Add $7$ and $5$ .

$- 2 v = 12$

Step 5

Divide each term in $- 2 v = 12$ by $- 2$ and simplify.

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Step 5.1

Divide each term in $- 2 v = 12$ by $- 2$ .

$\frac{- 2 v}{- 2} = \frac{12}{- 2}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 2$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 2 v}{- 2} = \frac{12}{- 2}$

Step 5.2.1.2

Divide $v$ by $1$ .

$v = \frac{12}{- 2}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $12$ by $- 2$ .

$v = - 6$