Algebra Examples

$4 = \frac{8}{v}$

Step 1

Subtract $\frac{8}{v}$ from both sides of the equation.

$4 - \frac{8}{v} = 0$

Step 2

Factor $4$ out of $4 - \frac{8}{v}$ .

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Step 2.1

Factor $4$ out of $4$ .

$4 (1) - \frac{8}{v} = 0$

Step 2.2

Factor $4$ out of $- \frac{8}{v}$ .

$4 (1) + 4 (- \frac{2}{v}) = 0$

Step 2.3

Factor $4$ out of $4 (1) + 4 (- \frac{2}{v})$ .

$4 (1 - \frac{2}{v}) = 0$

Step 3

Write $1$ as a fraction with a common denominator.

$4 (\frac{v}{v} - \frac{2}{v}) = 0$

Step 4

Combine the numerators over the common denominator.

$4 (\frac{v - 2}{v}) = 0$

Step 5

Combine $4$ and $\frac{v - 2}{v}$ .

$\frac{4 (v - 2)}{v} = 0$

Step 6

Set the numerator equal to zero.

$4 (v - 2) = 0$

Step 7

Solve the equation for $v$ .

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Step 7.1

Divide each term in $4 (v - 2) = 0$ by $4$ and simplify.

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Step 7.1.1

Divide each term in $4 (v - 2) = 0$ by $4$ .

$\frac{4 (v - 2)}{4} = \frac{0}{4}$

Step 7.1.2

Simplify the left side.

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Step 7.1.2.1

Cancel the common factor of $4$ .

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Step 7.1.2.1.1

Cancel the common factor.

$\frac{4 (v - 2)}{4} = \frac{0}{4}$

Step 7.1.2.1.2

Divide $v - 2$ by $1$ .

$v - 2 = \frac{0}{4}$

Step 7.1.3

Simplify the right side.

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Step 7.1.3.1

Divide $0$ by $4$ .

$v - 2 = 0$

Step 7.2

Add $2$ to both sides of the equation.

$v = 2$