Algebra Examples

3 + v = 2 (2 v - 1)

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

Step 1

Simplify

2 (2 v - 1)

$2 (2 v - 1)$ .

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Step 1.1

Rewrite.

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

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

Step 1.2

Simplify by adding zeros.

3 + v = 2 (2 v - 1)

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

Step 1.3

Apply the distributive property.

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

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

Step 1.4

Multiply.

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Step 1.4.1

Multiply

2

$2$ by

2

$2$ .

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

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

Step 1.4.2

Multiply

2

$2$ by

- 1

$- 1$ .

3 + v = 4 v - 2

$3 + v = 4 v - 2$

3 + v = 4 v - 2

$3 + v = 4 v - 2$

3 + v = 4 v - 2

$3 + v = 4 v - 2$

Step 2

Move all terms containing

v

$v$ to the left side of the equation.

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Step 2.1

Subtract

4 v

$4 v$ from both sides of the equation.

3 + v - 4 v = - 2

$3 + v - 4 v = - 2$

Step 2.2

Subtract

4 v

$4 v$ from

v

$v$ .

3 - 3 v = - 2

$3 - 3 v = - 2$

3 - 3 v = - 2

$3 - 3 v = - 2$

Step 3

Move all terms not containing

v

$v$ to the right side of the equation.

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Step 3.1

Subtract

3

$3$ from both sides of the equation.

- 3 v = - 2 - 3

$- 3 v = - 2 - 3$

Step 3.2

Subtract

3

$3$ from

- 2

$- 2$ .

- 3 v = - 5

$- 3 v = - 5$

- 3 v = - 5

$- 3 v = - 5$

Step 4

Divide each term in

- 3 v = - 5

$- 3 v = - 5$ by

- 3

$- 3$ and simplify.

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Step 4.1

Divide each term in

- 3 v = - 5

$- 3 v = - 5$ by

- 3

$- 3$ .

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

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of

- 3

$- 3$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide

$v$ by

$1$ .

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

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

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

Step 4.3

Simplify the right side.

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Step 4.3.1

Dividing two negative values results in a positive value.

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

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

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

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:

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

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$