Basic Math Examples

$- \frac{7}{v + 7} = - 8$

Step 1

Find the LCD of the terms in the equation.

Tap for more steps...

Step 1.1

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

$v + 7, 1$

Step 1.2

Remove parentheses.

$v + 7, 1$

Step 1.3

The LCM of one and any expression is the expression.

$v + 7$

Step 2

Multiply each term in $- \frac{7}{v + 7} = - 8$ by $v + 7$ to eliminate the fractions.

Tap for more steps...

Step 2.1

Multiply each term in $- \frac{7}{v + 7} = - 8$ by $v + 7$ .

$- \frac{7}{v + 7} (v + 7) = - 8 (v + 7)$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $v + 7$ .

Tap for more steps...

Step 2.2.1.1

Move the leading negative in $- \frac{7}{v + 7}$ into the numerator.

$\frac{- 7}{v + 7} (v + 7) = - 8 (v + 7)$

Step 2.2.1.2

Cancel the common factor.

$\frac{- 7}{v + 7} (v + 7) = - 8 (v + 7)$

Step 2.2.1.3

Rewrite the expression.

$- 7 = - 8 (v + 7)$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Apply the distributive property.

$- 7 = - 8 v - 8 \cdot 7$

Step 2.3.2

Multiply $- 8$ by $7$ .

$- 7 = - 8 v - 56$

Step 3

Solve the equation.

Tap for more steps...

Step 3.1

Rewrite the equation as $- 8 v - 56 = - 7$ .

$- 8 v - 56 = - 7$

Step 3.2

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

Tap for more steps...

Step 3.2.1

Add $56$ to both sides of the equation.

$- 8 v = - 7 + 56$

Step 3.2.2

Add $- 7$ and $56$ .

$- 8 v = 49$

Step 3.3

Divide each term in $- 8 v = 49$ by $- 8$ and simplify.

Tap for more steps...

Step 3.3.1

Divide each term in $- 8 v = 49$ by $- 8$ .

$\frac{- 8 v}{- 8} = \frac{49}{- 8}$

Step 3.3.2

Simplify the left side.

Tap for more steps...

Step 3.3.2.1

Cancel the common factor of $- 8$ .

Tap for more steps...

Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 8 v}{- 8} = \frac{49}{- 8}$

Step 3.3.2.1.2

Divide $v$ by $1$ .

$v = \frac{49}{- 8}$

Step 3.3.3

Simplify the right side.

Tap for more steps...

Step 3.3.3.1

Move the negative in front of the fraction.

$v = - \frac{49}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$v = - \frac{49}{8}$

Decimal Form:

$v = - 6.125$

Mixed Number Form:

$v = - 6 \frac{1}{8}$