Basic Math Examples

$\frac{8 v - 9}{5} - \frac{8 v + 8}{3} = - 13$

Step 1

Simplify $\frac{8 v - 9}{5} - \frac{8 v + 8}{3}$ .

Tap for more steps...

Step 1.1

Factor $8$ out of $8 v + 8$ .

Tap for more steps...

Step 1.1.1

Factor $8$ out of $8 v$ .

$\frac{8 v - 9}{5} - \frac{8 (v) + 8}{3} = - 13$

Step 1.1.2

Factor $8$ out of $8$ .

$\frac{8 v - 9}{5} - \frac{8 (v) + 8 (1)}{3} = - 13$

Step 1.1.3

Factor $8$ out of $8 (v) + 8 (1)$ .

$\frac{8 v - 9}{5} - \frac{8 (v + 1)}{3} = - 13$

Step 1.2

To write $\frac{8 v - 9}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{8 v - 9}{5} \cdot \frac{3}{3} - \frac{8 (v + 1)}{3} = - 13$

Step 1.3

To write $- \frac{8 (v + 1)}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{8 v - 9}{5} \cdot \frac{3}{3} - \frac{8 (v + 1)}{3} \cdot \frac{5}{5} = - 13$

Step 1.4

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 1.4.1

Multiply $\frac{8 v - 9}{5}$ by $\frac{3}{3}$ .

$\frac{(8 v - 9) \cdot 3}{5 \cdot 3} - \frac{8 (v + 1)}{3} \cdot \frac{5}{5} = - 13$

Step 1.4.2

Multiply $5$ by $3$ .

$\frac{(8 v - 9) \cdot 3}{15} - \frac{8 (v + 1)}{3} \cdot \frac{5}{5} = - 13$

Step 1.4.3

Multiply $\frac{8 (v + 1)}{3}$ by $\frac{5}{5}$ .

$\frac{(8 v - 9) \cdot 3}{15} - \frac{8 (v + 1) \cdot 5}{3 \cdot 5} = - 13$

Step 1.4.4

Multiply $3$ by $5$ .

$\frac{(8 v - 9) \cdot 3}{15} - \frac{8 (v + 1) \cdot 5}{15} = - 13$

Step 1.5

Combine the numerators over the common denominator.

$\frac{(8 v - 9) \cdot 3 - 8 (v + 1) \cdot 5}{15} = - 13$

Step 1.6

Simplify the numerator.

Tap for more steps...

Step 1.6.1

Apply the distributive property.

$\frac{8 v \cdot 3 - 9 \cdot 3 - 8 (v + 1) \cdot 5}{15} = - 13$

Step 1.6.2

Multiply $3$ by $8$ .

$\frac{24 v - 9 \cdot 3 - 8 (v + 1) \cdot 5}{15} = - 13$

Step 1.6.3

Multiply $- 9$ by $3$ .

$\frac{24 v - 27 - 8 (v + 1) \cdot 5}{15} = - 13$

Step 1.6.4

Apply the distributive property.

$\frac{24 v - 27 + (- 8 v - 8 \cdot 1) \cdot 5}{15} = - 13$

Step 1.6.5

Multiply $- 8$ by $1$ .

$\frac{24 v - 27 + (- 8 v - 8) \cdot 5}{15} = - 13$

Step 1.6.6

Apply the distributive property.

$\frac{24 v - 27 - 8 v \cdot 5 - 8 \cdot 5}{15} = - 13$

Step 1.6.7

Multiply $5$ by $- 8$ .

$\frac{24 v - 27 - 40 v - 8 \cdot 5}{15} = - 13$

Step 1.6.8

Multiply $- 8$ by $5$ .

$\frac{24 v - 27 - 40 v - 40}{15} = - 13$

Step 1.6.9

Subtract $40 v$ from $24 v$ .

$\frac{- 16 v - 27 - 40}{15} = - 13$

Step 1.6.10

Subtract $40$ from $- 27$ .

$\frac{- 16 v - 67}{15} = - 13$

Step 1.7

Simplify with factoring out.

Tap for more steps...

Step 1.7.1

Factor $- 1$ out of $- 16 v$ .

$\frac{- (16 v) - 67}{15} = - 13$

Step 1.7.2

Rewrite $- 67$ as $- 1 (67)$ .

$\frac{- (16 v) - 1 (67)}{15} = - 13$

Step 1.7.3

Factor $- 1$ out of $- (16 v) - 1 (67)$ .

$\frac{- (16 v + 67)}{15} = - 13$

Step 1.7.4

Simplify the expression.

Tap for more steps...

Step 1.7.4.1

Rewrite $- (16 v + 67)$ as $- 1 (16 v + 67)$ .

$\frac{- 1 (16 v + 67)}{15} = - 13$

Step 1.7.4.2

Move the negative in front of the fraction.

$- \frac{16 v + 67}{15} = - 13$

Step 2

Multiply both sides of the equation by $- 15$ .

$- 15 (- \frac{16 v + 67}{15}) = - 15 \cdot - 13$

Step 3

Simplify both sides of the equation.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

Simplify $- 15 (- \frac{16 v + 67}{15})$ .

Tap for more steps...

Step 3.1.1.1

Cancel the common factor of $15$ .

Tap for more steps...

Step 3.1.1.1.1

Move the leading negative in $- \frac{16 v + 67}{15}$ into the numerator.

$- 15 \frac{- (16 v + 67)}{15} = - 15 \cdot - 13$

Step 3.1.1.1.2

Factor $15$ out of $- 15$ .

$15 (- 1) \frac{- (16 v + 67)}{15} = - 15 \cdot - 13$

Step 3.1.1.1.3

Cancel the common factor.

$15 \cdot - 1 \frac{- (16 v + 67)}{15} = - 15 \cdot - 13$

Step 3.1.1.1.4

Rewrite the expression.

$- - (16 v + 67) = - 15 \cdot - 13$

Step 3.1.1.2

Multiply.

Tap for more steps...

Step 3.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 (16 v + 67) = - 15 \cdot - 13$

Step 3.1.1.2.2

Multiply $16 v + 67$ by $1$ .

$16 v + 67 = - 15 \cdot - 13$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Multiply $- 15$ by $- 13$ .

$16 v + 67 = 195$

Step 4

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

Tap for more steps...

Step 4.1

Subtract $67$ from both sides of the equation.

$16 v = 195 - 67$

Step 4.2

Subtract $67$ from $195$ .

$16 v = 128$

Step 5

Divide each term in $16 v = 128$ by $16$ and simplify.

Tap for more steps...

Step 5.1

Divide each term in $16 v = 128$ by $16$ .

$\frac{16 v}{16} = \frac{128}{16}$

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Cancel the common factor of $16$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor.

$\frac{16 v}{16} = \frac{128}{16}$

Step 5.2.1.2

Divide $v$ by $1$ .

$v = \frac{128}{16}$

Step 5.3

Simplify the right side.

Tap for more steps...

Step 5.3.1

Divide $128$ by $16$ .

$v = 8$