Pre-Algebra Examples

$- \frac{4}{v - 6} = 7$

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.

$v - 6, 1$

Step 1.2

Remove parentheses.

$v - 6, 1$

Step 1.3

The LCM of one and any expression is the expression.

$v - 6$

Step 2

Multiply each term in $- \frac{4}{v - 6} = 7$ by $v - 6$ to eliminate the fractions.

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Step 2.1

Multiply each term in $- \frac{4}{v - 6} = 7$ by $v - 6$ .

$- \frac{4}{v - 6} (v - 6) = 7 (v - 6)$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $v - 6$ .

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Step 2.2.1.1

Move the leading negative in $- \frac{4}{v - 6}$ into the numerator.

$\frac{- 4}{v - 6} (v - 6) = 7 (v - 6)$

Step 2.2.1.2

Cancel the common factor.

$\frac{- 4}{v - 6} (v - 6) = 7 (v - 6)$

Step 2.2.1.3

Rewrite the expression.

$- 4 = 7 (v - 6)$

Step 2.3

Simplify the right side.

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Step 2.3.1

Apply the distributive property.

$- 4 = 7 v + 7 \cdot - 6$

Step 2.3.2

Multiply $7$ by $- 6$ .

$- 4 = 7 v - 42$

Step 3

Solve the equation.

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Step 3.1

Rewrite the equation as $7 v - 42 = - 4$ .

$7 v - 42 = - 4$

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 $42$ to both sides of the equation.

$7 v = - 4 + 42$

Step 3.2.2

Add $- 4$ and $42$ .

$7 v = 38$

Step 3.3

Divide each term in $7 v = 38$ by $7$ and simplify.

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Step 3.3.1

Divide each term in $7 v = 38$ by $7$ .

$\frac{7 v}{7} = \frac{38}{7}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $7$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{7 v}{7} = \frac{38}{7}$

Step 3.3.2.1.2

Divide $v$ by $1$ .

$v = \frac{38}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$v = \frac{38}{7}$

Decimal Form:

$v = 5.\overline{428571}$

Mixed Number Form:

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