Basic Math Examples

$\frac{9 y + 4}{3} = \frac{5 y - 4}{6} + 15$

Step 1

Multiply both sides by $3$ .

$\frac{9 y + 4}{3} \cdot 3 = (\frac{5 y - 4}{6} + 15) \cdot 3$

Step 2

Simplify.

Tap for more steps...

Step 2.1

Simplify the left side.

Tap for more steps...

Step 2.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.1.1.1

Cancel the common factor.

$\frac{9 y + 4}{3} \cdot 3 = (\frac{5 y - 4}{6} + 15) \cdot 3$

Step 2.1.1.2

Rewrite the expression.

$9 y + 4 = (\frac{5 y - 4}{6} + 15) \cdot 3$

Step 2.2

Simplify the right side.

Tap for more steps...

Step 2.2.1

Simplify $(\frac{5 y - 4}{6} + 15) \cdot 3$ .

Tap for more steps...

Step 2.2.1.1

To write $15$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$9 y + 4 = (\frac{5 y - 4}{6} + 15 \cdot \frac{6}{6}) \cdot 3$

Step 2.2.1.2

Simplify terms.

Tap for more steps...

Step 2.2.1.2.1

Combine $15$ and $\frac{6}{6}$ .

$9 y + 4 = (\frac{5 y - 4}{6} + \frac{15 \cdot 6}{6}) \cdot 3$

Step 2.2.1.2.2

Combine the numerators over the common denominator.

$9 y + 4 = \frac{5 y - 4 + 15 \cdot 6}{6} \cdot 3$

Step 2.2.1.3

Simplify the numerator.

Tap for more steps...

Step 2.2.1.3.1

Multiply $15$ by $6$ .

$9 y + 4 = \frac{5 y - 4 + 90}{6} \cdot 3$

Step 2.2.1.3.2

Add $- 4$ and $90$ .

$9 y + 4 = \frac{5 y + 86}{6} \cdot 3$

Step 2.2.1.4

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.2.1.4.1

Factor $3$ out of $6$ .

$9 y + 4 = \frac{5 y + 86}{3 (2)} \cdot 3$

Step 2.2.1.4.2

Cancel the common factor.

$9 y + 4 = \frac{5 y + 86}{3 \cdot 2} \cdot 3$

Step 2.2.1.4.3

Rewrite the expression.

$9 y + 4 = \frac{5 y + 86}{2}$

Step 3

Solve for $y$ .

Tap for more steps...

Step 3.1

Multiply both sides by $2$ .

$(9 y + 4) \cdot 2 = \frac{5 y + 86}{2} \cdot 2$

Step 3.2

Simplify.

Tap for more steps...

Step 3.2.1

Simplify the left side.

Tap for more steps...

Step 3.2.1.1

Simplify $(9 y + 4) \cdot 2$ .

Tap for more steps...

Step 3.2.1.1.1

Apply the distributive property.

$9 y \cdot 2 + 4 \cdot 2 = \frac{5 y + 86}{2} \cdot 2$

Step 3.2.1.1.2

Multiply.

Tap for more steps...

Step 3.2.1.1.2.1

Multiply $2$ by $9$ .

$18 y + 4 \cdot 2 = \frac{5 y + 86}{2} \cdot 2$

Step 3.2.1.1.2.2

Multiply $4$ by $2$ .

$18 y + 8 = \frac{5 y + 86}{2} \cdot 2$

Step 3.2.2

Simplify the right side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

$18 y + 8 = \frac{5 y + 86}{2} \cdot 2$

Step 3.2.2.1.2

Rewrite the expression.

$18 y + 8 = 5 y + 86$

Step 3.3

Solve for $y$ .

Tap for more steps...

Step 3.3.1

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

Tap for more steps...

Step 3.3.1.1

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

$18 y + 8 - 5 y = 86$

Step 3.3.1.2

Subtract $5 y$ from $18 y$ .

$13 y + 8 = 86$

Step 3.3.2

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

Tap for more steps...

Step 3.3.2.1

Subtract $8$ from both sides of the equation.

$13 y = 86 - 8$

Step 3.3.2.2

Subtract $8$ from $86$ .

$13 y = 78$

Step 3.3.3

Divide each term in $13 y = 78$ by $13$ and simplify.

Tap for more steps...

Step 3.3.3.1

Divide each term in $13 y = 78$ by $13$ .

$\frac{13 y}{13} = \frac{78}{13}$

Step 3.3.3.2

Simplify the left side.

Tap for more steps...

Step 3.3.3.2.1

Cancel the common factor of $13$ .

Tap for more steps...

Step 3.3.3.2.1.1

Cancel the common factor.

$\frac{13 y}{13} = \frac{78}{13}$

Step 3.3.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{78}{13}$

Step 3.3.3.3

Simplify the right side.

Tap for more steps...

Step 3.3.3.3.1

Divide $78$ by $13$ .

$y = 6$