Finite Math Examples

$\frac{3 y}{4} - 4 = \frac{y}{2} + 5$

Step 1

Move all terms containing $y$ to the left side of the equation.

Tap for more steps...

Step 1.1

Subtract $\frac{y}{2}$ from both sides of the equation.

$\frac{3 y}{4} - 4 - \frac{y}{2} = 5$

Step 1.2

To write $- \frac{y}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 y}{4} - \frac{y}{2} \cdot \frac{2}{2} - 4 = 5$

Step 1.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 1.3.1

Multiply $\frac{y}{2}$ by $\frac{2}{2}$ .

$\frac{3 y}{4} - \frac{y \cdot 2}{2 \cdot 2} - 4 = 5$

Step 1.3.2

Multiply $2$ by $2$ .

$\frac{3 y}{4} - \frac{y \cdot 2}{4} - 4 = 5$

Step 1.4

Combine the numerators over the common denominator.

$\frac{3 y - y \cdot 2}{4} - 4 = 5$

Step 1.5

Simplify each term.

Tap for more steps...

Step 1.5.1

Simplify the numerator.

Tap for more steps...

Step 1.5.1.1

Factor $y$ out of $3 y - y \cdot 2$ .

Tap for more steps...

Step 1.5.1.1.1

Factor $y$ out of $3 y$ .

$\frac{y \cdot 3 - y \cdot 2}{4} - 4 = 5$

Step 1.5.1.1.2

Factor $y$ out of $- y \cdot 2$ .

$\frac{y \cdot 3 + y (- 1 \cdot 2)}{4} - 4 = 5$

Step 1.5.1.1.3

Factor $y$ out of $y \cdot 3 + y (- 1 \cdot 2)$ .

$\frac{y (3 - 1 \cdot 2)}{4} - 4 = 5$

Step 1.5.1.2

Multiply $- 1$ by $2$ .

$\frac{y (3 - 2)}{4} - 4 = 5$

Step 1.5.1.3

Subtract $2$ from $3$ .

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

Step 1.5.2

Multiply $y$ by $1$ .

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

Step 2

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

Tap for more steps...

Step 2.1

Add $4$ to both sides of the equation.

$\frac{y}{4} = 5 + 4$

Step 2.2

Add $5$ and $4$ .

$\frac{y}{4} = 9$

Step 3

Multiply both sides of the equation by $4$ .

$4 \frac{y}{4} = 4 \cdot 9$

Step 4

Simplify both sides of the equation.

Tap for more steps...

Step 4.1

Simplify the left side.

Tap for more steps...

Step 4.1.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 4.1.1.1

Cancel the common factor.

$4 \frac{y}{4} = 4 \cdot 9$

Step 4.1.1.2

Rewrite the expression.

$y = 4 \cdot 9$

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Multiply $4$ by $9$ .

$y = 36$