Finite Math Examples

$\frac{5}{v + 2} = - 2$

Step 1

Find the LCD of the terms in the equation.

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Step 1.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$v + 2, 1$

Step 1.2

Remove parentheses.

$v + 2, 1$

Step 1.3

The LCM of one and any expression is the expression.

$v + 2$

Step 2

Multiply each term in $\frac{5}{v + 2} = - 2$ by $v + 2$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{5}{v + 2} = - 2$ by $v + 2$ .

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $v + 2$ .

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Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Rewrite the expression.

$5 = - 2 (v + 2)$

Step 2.3

Simplify the right side.

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Step 2.3.1

Apply the distributive property.

$5 = - 2 v - 2 \cdot 2$

Step 2.3.2

Multiply $- 2$ by $2$ .

$5 = - 2 v - 4$

Step 3

Solve the equation.

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Step 3.1

Rewrite the equation as $- 2 v - 4 = 5$ .

$- 2 v - 4 = 5$

Step 3.2

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

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Step 3.2.1

Add $4$ to both sides of the equation.

$- 2 v = 5 + 4$

Step 3.2.2

Add $5$ and $4$ .

$- 2 v = 9$

Step 3.3

Divide each term in $- 2 v = 9$ by $- 2$ and simplify.

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Step 3.3.1

Divide each term in $- 2 v = 9$ by $- 2$ .

$\frac{- 2 v}{- 2} = \frac{9}{- 2}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 2$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 2 v}{- 2} = \frac{9}{- 2}$

Step 3.3.2.1.2

Divide $v$ by $1$ .

$v = \frac{9}{- 2}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Move the negative in front of the fraction.

$v = - \frac{9}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$v = - \frac{9}{2}$

Decimal Form:

$v = - 4.5$

Mixed Number Form:

$v = - 4 \frac{1}{2}$