Basic Math Examples

$\frac{v a - 8}{20} + 0.4 + \frac{v a}{10} + \frac{v a + 4}{10} = 0$

Step 1

Simplify $\frac{v a - 8}{20} + 0.4 + \frac{v a}{10} + \frac{v a + 4}{10}$ .

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Step 1.1

Combine the numerators over the common denominator.

$0.4 + \frac{v a - 8}{20} + \frac{v a + v a + 4}{10} = 0$

Step 1.2

Add $v a$ and $v a$ .

$0.4 + \frac{v a - 8}{20} + \frac{2 v a + 4}{10} = 0$

Step 1.3

Cancel the common factor of $2 v a + 4$ and $10$ .

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Step 1.3.1

Factor $2$ out of $2 v a$ .

$0.4 + \frac{v a - 8}{20} + \frac{2 (v a) + 4}{10} = 0$

Step 1.3.2

Factor $2$ out of $4$ .

$0.4 + \frac{v a - 8}{20} + \frac{2 (v a) + 2 \cdot 2}{10} = 0$

Step 1.3.3

Factor $2$ out of $2 (v a) + 2 \cdot 2$ .

$0.4 + \frac{v a - 8}{20} + \frac{2 (v a + 2)}{10} = 0$

Step 1.3.4

Cancel the common factors.

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Step 1.3.4.1

Factor $2$ out of $10$ .

$0.4 + \frac{v a - 8}{20} + \frac{2 (v a + 2)}{2 (5)} = 0$

Step 1.3.4.2

Cancel the common factor.

$0.4 + \frac{v a - 8}{20} + \frac{2 (v a + 2)}{2 \cdot 5} = 0$

Step 1.3.4.3

Rewrite the expression.

$0.4 + \frac{v a - 8}{20} + \frac{v a + 2}{5} = 0$

Step 1.4

To write $0.4$ as a fraction with a common denominator, multiply by $\frac{20}{20}$ .

$0.4 \cdot \frac{20}{20} + \frac{v a - 8}{20} + \frac{v a + 2}{5} = 0$

Step 1.5

Combine $0.4$ and $\frac{20}{20}$ .

$\frac{0.4 \cdot 20}{20} + \frac{v a - 8}{20} + \frac{v a + 2}{5} = 0$

Step 1.6

Combine the numerators over the common denominator.

$\frac{0.4 \cdot 20 + v a - 8}{20} + \frac{v a + 2}{5} = 0$

Step 1.7

Simplify the expression.

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Step 1.7.1

Multiply $0.4$ by $20$ .

$\frac{8 + v a - 8}{20} + \frac{v a + 2}{5} = 0$

Step 1.7.2

Subtract $8$ from $8$ .

$\frac{v a + 0}{20} + \frac{v a + 2}{5} = 0$

Step 1.7.3

Add $v a$ and $0$ .

$\frac{v a}{20} + \frac{v a + 2}{5} = 0$

Step 1.8

To write $\frac{v a + 2}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{v a}{20} + \frac{v a + 2}{5} \cdot \frac{4}{4} = 0$

Step 1.9

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.9.1

Multiply $\frac{v a + 2}{5}$ by $\frac{4}{4}$ .

$\frac{v a}{20} + \frac{(v a + 2) \cdot 4}{5 \cdot 4} = 0$

Step 1.9.2

Multiply $5$ by $4$ .

$\frac{v a}{20} + \frac{(v a + 2) \cdot 4}{20} = 0$

Step 1.10

Combine the numerators over the common denominator.

$\frac{v a + (v a + 2) \cdot 4}{20} = 0$

Step 1.11

Simplify the numerator.

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Step 1.11.1

Apply the distributive property.

$\frac{v a + v a \cdot 4 + 2 \cdot 4}{20} = 0$

Step 1.11.2

Move $4$ to the left of $v a$ .

$\frac{v a + 4 \cdot (v a) + 2 \cdot 4}{20} = 0$

Step 1.11.3

Multiply $2$ by $4$ .

$\frac{v a + 4 \cdot (v a) + 8}{20} = 0$

Step 1.11.4

Remove parentheses.

$\frac{v a + 4 v a + 8}{20} = 0$

Step 1.11.5

Add $v a$ and $4 v a$ .

$\frac{5 v a + 8}{20} = 0$

Step 2

Set the numerator equal to zero.

$5 v a + 8 = 0$

Step 3

Solve the equation for $v$ .

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Step 3.1

Subtract $8$ from both sides of the equation.

$5 v a = - 8$

Step 3.2

Divide each term in $5 v a = - 8$ by $5 a$ and simplify.

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Step 3.2.1

Divide each term in $5 v a = - 8$ by $5 a$ .

$\frac{5 v a}{5 a} = \frac{- 8}{5 a}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $5$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{5 v a}{5 a} = \frac{- 8}{5 a}$

Step 3.2.2.1.2

Rewrite the expression.

$\frac{v a}{a} = \frac{- 8}{5 a}$

Step 3.2.2.2

Cancel the common factor of $a$ .

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Step 3.2.2.2.1

Cancel the common factor.

$\frac{v a}{a} = \frac{- 8}{5 a}$

Step 3.2.2.2.2

Divide $v$ by $1$ .

$v = \frac{- 8}{5 a}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Move the negative in front of the fraction.

$v = - \frac{8}{5 a}$