Basic Math Examples

$3 y + 9 = \frac{1}{4} y$

Step 1

Simplify $\frac{1}{4} y$ .

Tap for more steps...

Step 1.1

Rewrite.

$3 y + 9 = 0 + 0 + \frac{1}{4} y$

Step 1.2

Simplify by adding zeros.

$3 y + 9 = \frac{1}{4} y$

Step 1.3

Combine $\frac{1}{4}$ and $y$ .

$3 y + 9 = \frac{y}{4}$

Step 2

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

Tap for more steps...

Step 2.1

Subtract $\frac{y}{4}$ from both sides of the equation.

$3 y + 9 - \frac{y}{4} = 0$

Step 2.2

To write $3 y$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$3 y \cdot \frac{4}{4} - \frac{y}{4} + 9 = 0$

Step 2.3

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

$\frac{3 y \cdot 4}{4} - \frac{y}{4} + 9 = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{3 y \cdot 4 - y}{4} + 9 = 0$

Step 2.5

Simplify each term.

Tap for more steps...

Step 2.5.1

Simplify the numerator.

Tap for more steps...

Step 2.5.1.1

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

Tap for more steps...

Step 2.5.1.1.1

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

$\frac{y (3 \cdot 4) - y}{4} + 9 = 0$

Step 2.5.1.1.2

Factor $y$ out of $- y$ .

$\frac{y (3 \cdot 4) + y \cdot - 1}{4} + 9 = 0$

Step 2.5.1.1.3

Factor $y$ out of $y (3 \cdot 4) + y \cdot - 1$ .

$\frac{y (3 \cdot 4 - 1)}{4} + 9 = 0$

Step 2.5.1.2

Multiply $3$ by $4$ .

$\frac{y (12 - 1)}{4} + 9 = 0$

Step 2.5.1.3

Subtract $1$ from $12$ .

$\frac{y \cdot 11}{4} + 9 = 0$

Step 2.5.2

Move $11$ to the left of $y$ .

$\frac{11 y}{4} + 9 = 0$

Step 3

Subtract $9$ from both sides of the equation.

$\frac{11 y}{4} = - 9$

Step 4

Multiply both sides of the equation by $\frac{4}{11}$ .

$\frac{4}{11} \cdot \frac{11 y}{4} = \frac{4}{11} \cdot - 9$

Step 5

Simplify both sides of the equation.

Tap for more steps...

Step 5.1

Simplify the left side.

Tap for more steps...

Step 5.1.1

Simplify $\frac{4}{11} \cdot \frac{11 y}{4}$ .

Tap for more steps...

Step 5.1.1.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 5.1.1.1.1

Cancel the common factor.

$\frac{4}{11} \cdot \frac{11 y}{4} = \frac{4}{11} \cdot - 9$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{11} (11 y) = \frac{4}{11} \cdot - 9$

Step 5.1.1.2

Cancel the common factor of $11$ .

Tap for more steps...

Step 5.1.1.2.1

Factor $11$ out of $11 y$ .

$\frac{1}{11} (11 (y)) = \frac{4}{11} \cdot - 9$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{11} (11 y) = \frac{4}{11} \cdot - 9$

Step 5.1.1.2.3

Rewrite the expression.

$y = \frac{4}{11} \cdot - 9$

Step 5.2

Simplify the right side.

Tap for more steps...

Step 5.2.1

Simplify $\frac{4}{11} \cdot - 9$ .

Tap for more steps...

Step 5.2.1.1

Multiply $\frac{4}{11} \cdot - 9$ .

Tap for more steps...

Step 5.2.1.1.1

Combine $\frac{4}{11}$ and $- 9$ .

$y = \frac{4 \cdot - 9}{11}$

Step 5.2.1.1.2

Multiply $4$ by $- 9$ .

$y = \frac{- 36}{11}$

Step 5.2.1.2

Move the negative in front of the fraction.

$y = - \frac{36}{11}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{36}{11}$

Decimal Form:

$y = - 3.\overline{27}$

Mixed Number Form:

$y = - 3 \frac{3}{11}$