Finite Math Examples

$\frac{2}{3} y = 3 - \frac{5}{6} y$

Step 1

Solve for $y$ .

Tap for more steps...

Step 1.1

Simplify $\frac{2}{3} y$ .

Tap for more steps...

Step 1.1.1

Rewrite.

$0 + 0 + \frac{2}{3} y = 3 - \frac{5}{6} y$

Step 1.1.2

Simplify by adding zeros.

$\frac{2}{3} y = 3 - \frac{5}{6} y$

Step 1.1.3

Combine $\frac{2}{3}$ and $y$ .

$\frac{2 y}{3} = 3 - \frac{5}{6} y$

Step 1.2

Simplify each term.

Tap for more steps...

Step 1.2.1

Combine $y$ and $\frac{5}{6}$ .

$\frac{2 y}{3} = 3 - \frac{y \cdot 5}{6}$

Step 1.2.2

Move $5$ to the left of $y$ .

$\frac{2 y}{3} = 3 - \frac{5 y}{6}$

Step 1.3

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

Tap for more steps...

Step 1.3.1

Add $\frac{5 y}{6}$ to both sides of the equation.

$\frac{2 y}{3} + \frac{5 y}{6} = 3$

Step 1.3.2

To write $\frac{2 y}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2 y}{3} \cdot \frac{2}{2} + \frac{5 y}{6} = 3$

Step 1.3.3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 1.3.3.1

Multiply $\frac{2 y}{3}$ by $\frac{2}{2}$ .

$\frac{2 y \cdot 2}{3 \cdot 2} + \frac{5 y}{6} = 3$

Step 1.3.3.2

Multiply $3$ by $2$ .

$\frac{2 y \cdot 2}{6} + \frac{5 y}{6} = 3$

Step 1.3.4

Combine the numerators over the common denominator.

$\frac{2 y \cdot 2 + 5 y}{6} = 3$

Step 1.3.5

Simplify the numerator.

Tap for more steps...

Step 1.3.5.1

Factor $y$ out of $2 y \cdot 2 + 5 y$ .

Tap for more steps...

Step 1.3.5.1.1

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

$\frac{y (2 \cdot 2) + 5 y}{6} = 3$

Step 1.3.5.1.2

Factor $y$ out of $5 y$ .

$\frac{y (2 \cdot 2) + y \cdot 5}{6} = 3$

Step 1.3.5.1.3

Factor $y$ out of $y (2 \cdot 2) + y \cdot 5$ .

$\frac{y (2 \cdot 2 + 5)}{6} = 3$

Step 1.3.5.2

Multiply $2$ by $2$ .

$\frac{y (4 + 5)}{6} = 3$

Step 1.3.5.3

Add $4$ and $5$ .

$\frac{y \cdot 9}{6} = 3$

Step 1.3.6

Cancel the common factor of $9$ and $6$ .

Tap for more steps...

Step 1.3.6.1

Factor $3$ out of $y \cdot 9$ .

$\frac{3 (y \cdot 3)}{6} = 3$

Step 1.3.6.2

Cancel the common factors.

Tap for more steps...

Step 1.3.6.2.1

Factor $3$ out of $6$ .

$\frac{3 (y \cdot 3)}{3 (2)} = 3$

Step 1.3.6.2.2

Cancel the common factor.

$\frac{3 (y \cdot 3)}{3 \cdot 2} = 3$

Step 1.3.6.2.3

Rewrite the expression.

$\frac{y \cdot 3}{2} = 3$

Step 1.3.7

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

$\frac{3 y}{2} = 3$

Step 1.4

Multiply both sides of the equation by $\frac{2}{3}$ .

$\frac{2}{3} \cdot \frac{3 y}{2} = \frac{2}{3} \cdot 3$

Step 1.5

Simplify both sides of the equation.

Tap for more steps...

Step 1.5.1

Simplify the left side.

Tap for more steps...

Step 1.5.1.1

Simplify $\frac{2}{3} \cdot \frac{3 y}{2}$ .

Tap for more steps...

Step 1.5.1.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.5.1.1.1.1

Cancel the common factor.

$\frac{2}{3} \cdot \frac{3 y}{2} = \frac{2}{3} \cdot 3$

Step 1.5.1.1.1.2

Rewrite the expression.

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

Step 1.5.1.1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.5.1.1.2.1

Factor $3$ out of $3 y$ .

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

Step 1.5.1.1.2.2

Cancel the common factor.

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

Step 1.5.1.1.2.3

Rewrite the expression.

$y = \frac{2}{3} \cdot 3$

Step 1.5.2

Simplify the right side.

Tap for more steps...

Step 1.5.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.5.2.1.1

Cancel the common factor.

$y = \frac{2}{3} \cdot 3$

Step 1.5.2.1.2

Rewrite the expression.

$y = 2$

Step 2

Set $3 - \frac{5}{6} y$ equal to $0$ .

$2 = 0$

Step 3

Since $2 \neq 0$ , there are no solutions.

No solution