Solve for v 3+v=2(2v-1)

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

Step 1

Simplify $2 (2 v - 1)$ .

Rewrite.

$3 + v = 0 + 0 + 2 (2 v - 1)$

Simplify by adding zeros.

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

Apply the distributive property.

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

Multiply.

Multiply $2$ by $2$ .

$3 + v = 4 v + 2 \cdot - 1$

Multiply $2$ by $- 1$ .

$3 + v = 4 v - 2$

Step 2

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

Subtract $4 v$ from both sides of the equation.

$3 + v - 4 v = - 2$

Subtract $4 v$ from $v$ .

$3 - 3 v = - 2$

Step 3

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

Subtract $3$ from both sides of the equation.

$- 3 v = - 2 - 3$

Subtract $3$ from $- 2$ .

$- 3 v = - 5$

Step 4

Divide each term in $- 3 v = - 5$ by $- 3$ and simplify.

Divide each term in $- 3 v = - 5$ by $- 3$ .

$\frac{- 3 v}{- 3} = \frac{- 5}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 v}{- 3} = \frac{- 5}{- 3}$

Divide $v$ by $1$ .

$v = \frac{- 5}{- 3}$

Simplify the right side.

Dividing two negative values results in a positive value.

$v = \frac{5}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$v = \frac{5}{3}$

Decimal Form:

$v = 1.\overline{6}$

Mixed Number Form:

$v = 1 \frac{2}{3}$

Solve for v 3+v=2(2v-1)

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