Basic Math Examples

$\frac{9 + 5 v}{2} + 3 = 20 v$

Step 1

Simplify $\frac{9 + 5 v}{2} + 3$ .

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Step 1.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{9 + 5 v}{2} + 3 \cdot \frac{2}{2} = 20 v$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine $3$ and $\frac{2}{2}$ .

$\frac{9 + 5 v}{2} + \frac{3 \cdot 2}{2} = 20 v$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{9 + 5 v + 3 \cdot 2}{2} = 20 v$

Step 1.3

Simplify the numerator.

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Step 1.3.1

Multiply $3$ by $2$ .

$\frac{9 + 5 v + 6}{2} = 20 v$

Step 1.3.2

Add $9$ and $6$ .

$\frac{5 v + 15}{2} = 20 v$

Step 1.3.3

Factor $5$ out of $5 v + 15$ .

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Step 1.3.3.1

Factor $5$ out of $5 v$ .

$\frac{5 (v) + 15}{2} = 20 v$

Step 1.3.3.2

Factor $5$ out of $15$ .

$\frac{5 v + 5 \cdot 3}{2} = 20 v$

Step 1.3.3.3

Factor $5$ out of $5 v + 5 \cdot 3$ .

$\frac{5 (v + 3)}{2} = 20 v$

Step 2

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

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Step 2.1

Subtract $20 v$ from both sides of the equation.

$\frac{5 (v + 3)}{2} - 20 v = 0$

Step 2.2

To write $- 20 v$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 (v + 3)}{2} - 20 v \cdot \frac{2}{2} = 0$

Step 2.3

Combine $- 20 v$ and $\frac{2}{2}$ .

$\frac{5 (v + 3)}{2} + \frac{- 20 v \cdot 2}{2} = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{5 (v + 3) - 20 v \cdot 2}{2} = 0$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Factor $5$ out of $5 (v + 3) - 20 v \cdot 2$ .

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Step 2.5.1.1

Factor $5$ out of $- 20 v \cdot 2$ .

$\frac{5 (v + 3) + 5 (- 4 v \cdot 2)}{2} = 0$

Step 2.5.1.2

Factor $5$ out of $5 (v + 3) + 5 (- 4 v \cdot 2)$ .

$\frac{5 (v + 3 - 4 v \cdot 2)}{2} = 0$

Step 2.5.2

Multiply $2$ by $- 4$ .

$\frac{5 (v + 3 - 8 v)}{2} = 0$

Step 2.5.3

Subtract $8 v$ from $v$ .

$\frac{5 (- 7 v + 3)}{2} = 0$

Step 2.6

Factor $- 1$ out of $- 7 v$ .

$\frac{5 (- (7 v) + 3)}{2} = 0$

Step 2.7

Rewrite $3$ as $- 1 (- 3)$ .

$\frac{5 (- (7 v) - 1 (- 3))}{2} = 0$

Step 2.8

Factor $- 1$ out of $- (7 v) - 1 (- 3)$ .

$\frac{5 (- (7 v - 3))}{2} = 0$

Step 2.9

Rewrite $- (7 v - 3)$ as $- 1 (7 v - 3)$ .

$\frac{5 (- 1 (7 v - 3))}{2} = 0$

Step 2.10

Move the negative in front of the fraction.

$- \frac{5 (7 v - 3)}{2} = 0$

Step 3

Set the numerator equal to zero.

$5 (7 v - 3) = 0$

Step 4

Solve the equation for $v$ .

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Step 4.1

Divide each term in $5 (7 v - 3) = 0$ by $5$ and simplify.

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Step 4.1.1

Divide each term in $5 (7 v - 3) = 0$ by $5$ .

$\frac{5 (7 v - 3)}{5} = \frac{0}{5}$

Step 4.1.2

Simplify the left side.

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Step 4.1.2.1

Cancel the common factor of $5$ .

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Step 4.1.2.1.1

Cancel the common factor.

$\frac{5 (7 v - 3)}{5} = \frac{0}{5}$

Step 4.1.2.1.2

Divide $7 v - 3$ by $1$ .

$7 v - 3 = \frac{0}{5}$

Step 4.1.3

Simplify the right side.

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Step 4.1.3.1

Divide $0$ by $5$ .

$7 v - 3 = 0$

Step 4.2

Add $3$ to both sides of the equation.

$7 v = 3$

Step 4.3

Divide each term in $7 v = 3$ by $7$ and simplify.

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Step 4.3.1

Divide each term in $7 v = 3$ by $7$ .

$\frac{7 v}{7} = \frac{3}{7}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $7$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{7 v}{7} = \frac{3}{7}$

Step 4.3.2.1.2

Divide $v$ by $1$ .

$v = \frac{3}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$v = \frac{3}{7}$

Decimal Form:

$v = 0.\overline{428571}$