Basic Math Examples

$v (\frac{3 y}{4} - 1) = 5 y - 3$

Step 1

Simplify $v (\frac{3 y}{4} - 1)$ .

Tap for more steps...

Step 1.1

Rewrite.

$0 + 0 + v (\frac{3 y}{4} - 1) = 5 y - 3$

Step 1.2

Simplify terms.

Tap for more steps...

Step 1.2.1

Apply the distributive property.

$v \frac{3 y}{4} + v \cdot - 1 = 5 y - 3$

Step 1.2.2

Combine $v$ and $\frac{3 y}{4}$ .

$\frac{v (3 y)}{4} + v \cdot - 1 = 5 y - 3$

Step 1.2.3

Move $- 1$ to the left of $v$ .

$\frac{v (3 y)}{4} - 1 \cdot v = 5 y - 3$

Step 1.3

Simplify each term.

Tap for more steps...

Step 1.3.1

Move $3$ to the left of $v$ .

$\frac{3 \cdot v y}{4} - 1 \cdot v = 5 y - 3$

Step 1.3.2

Rewrite $- 1 v$ as $- v$ .

$\frac{3 v y}{4} - v = 5 y - 3$

Step 2

Subtract $5 y$ from both sides of the equation.

$\frac{3 v y}{4} - v - 5 y = - 3$

Step 3

Add $v$ to both sides of the equation.

$\frac{3 v y}{4} - 5 y = - 3 + v$

Step 4

Factor $y$ out of $\frac{3 v y}{4} - 5 y$ .

Tap for more steps...

Step 4.1

Factor $y$ out of $\frac{3 v y}{4}$ .

$y (\frac{3 v}{4}) - 5 y = - 3 + v$

Step 4.2

Factor $y$ out of $- 5 y$ .

$y (\frac{3 v}{4}) + y \cdot - 5 = - 3 + v$

Step 4.3

Factor $y$ out of $y \frac{3 v}{4} + y \cdot - 5$ .

$y (\frac{3 v}{4} - 5) = - 3 + v$

Step 5

Divide each term in $y (\frac{3 v}{4} - 5) = - 3 + v$ by $\frac{3 v}{4} - 5$ and simplify.

Tap for more steps...

Step 5.1

Divide each term in $y (\frac{3 v}{4} - 5) = - 3 + v$ by $\frac{3 v}{4} - 5$ .

$\frac{y (\frac{3 v}{4} - 5)}{\frac{3 v}{4} - 5} = \frac{- 3}{\frac{3 v}{4} - 5} + \frac{v}{\frac{3 v}{4} - 5}$

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Cancel the common factor of $\frac{3 v}{4} - 5$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor.

$\frac{y (\frac{3 v}{4} - 5)}{\frac{3 v}{4} - 5} = \frac{- 3}{\frac{3 v}{4} - 5} + \frac{v}{\frac{3 v}{4} - 5}$

Step 5.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 3}{\frac{3 v}{4} - 5} + \frac{v}{\frac{3 v}{4} - 5}$

Step 5.3

Simplify the right side.

Tap for more steps...

Step 5.3.1

Combine the numerators over the common denominator.

$y = \frac{- 3 + v}{\frac{3 v}{4} - 5}$

Step 5.3.2

Multiply the numerator and denominator of the fraction by $4$ .

Tap for more steps...

Step 5.3.2.1

Multiply $\frac{- 3 + v}{\frac{3 v}{4} - 5}$ by $\frac{4}{4}$ .

$y = \frac{4}{4} \cdot \frac{- 3 + v}{\frac{3 v}{4} - 5}$

Step 5.3.2.2

Combine.

$y = \frac{4 (- 3 + v)}{4 (\frac{3 v}{4} - 5)}$

Step 5.3.3

Apply the distributive property.

$y = \frac{4 \cdot - 3 + 4 v}{4 \frac{3 v}{4} + 4 \cdot - 5}$

Step 5.3.4

Simplify terms.

Tap for more steps...

Step 5.3.4.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 5.3.4.1.1

Cancel the common factor.

$y = \frac{4 \cdot - 3 + 4 v}{4 \frac{3 v}{4} + 4 \cdot - 5}$

Step 5.3.4.1.2

Rewrite the expression.

$y = \frac{4 \cdot - 3 + 4 v}{3 v + 4 \cdot - 5}$

Step 5.3.4.2

Factor $4$ out of $4 \cdot - 3 + 4 v$ .

Tap for more steps...

Step 5.3.4.2.1

Factor $4$ out of $4 \cdot - 3$ .

$y = \frac{4 (- 3) + 4 v}{3 v + 4 \cdot - 5}$

Step 5.3.4.2.2

Factor $4$ out of $4 v$ .

$y = \frac{4 (- 3) + 4 (v)}{3 v + 4 \cdot - 5}$

Step 5.3.4.2.3

Factor $4$ out of $4 (- 3) + 4 (v)$ .

$y = \frac{4 (- 3 + v)}{3 v + 4 \cdot - 5}$

Step 5.3.4.3

Multiply $4$ by $- 5$ .

$y = \frac{4 (- 3 + v)}{3 v - 20}$

Step 5.3.4.4

Rewrite $- 3$ as $- 1 (3)$ .

$y = \frac{4 (- 1 (3) + v)}{3 v - 20}$

Step 5.3.4.5

Factor $- 1$ out of $v$ .

$y = \frac{4 (- 1 (3) - 1 (- v))}{3 v - 20}$

Step 5.3.4.6

Factor $- 1$ out of $- 1 (3) - 1 (- v)$ .

$y = \frac{4 (- 1 (3 - v))}{3 v - 20}$

Step 5.3.4.7

Move the negative in front of the fraction.

$y = - \frac{4 (3 - v)}{3 v - 20}$