Basic Math Examples

$\frac{6}{5} y - \frac{1}{2} = - 4 y + \frac{7}{5}$

Step 1

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

$\frac{6 y}{5} - \frac{1}{2} = - 4 y + \frac{7}{5}$

Step 2

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

Tap for more steps...

Step 2.1

Add $4 y$ to both sides of the equation.

$\frac{6 y}{5} - \frac{1}{2} + 4 y = \frac{7}{5}$

Step 2.2

To write $4 y$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{6 y}{5} + 4 y \cdot \frac{5}{5} - \frac{1}{2} = \frac{7}{5}$

Step 2.3

Combine $4 y$ and $\frac{5}{5}$ .

$\frac{6 y}{5} + \frac{4 y \cdot 5}{5} - \frac{1}{2} = \frac{7}{5}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{6 y + 4 y \cdot 5}{5} - \frac{1}{2} = \frac{7}{5}$

Step 2.5

Simplify the numerator.

Tap for more steps...

Step 2.5.1

Factor $2 y$ out of $6 y + 4 y \cdot 5$ .

Tap for more steps...

Step 2.5.1.1

Factor $2 y$ out of $6 y$ .

$\frac{2 y (3) + 4 y \cdot 5}{5} - \frac{1}{2} = \frac{7}{5}$

Step 2.5.1.2

Factor $2 y$ out of $4 y \cdot 5$ .

$\frac{2 y (3) + 2 y (2 \cdot 5)}{5} - \frac{1}{2} = \frac{7}{5}$

Step 2.5.1.3

Factor $2 y$ out of $2 y (3) + 2 y (2 \cdot 5)$ .

$\frac{2 y (3 + 2 \cdot 5)}{5} - \frac{1}{2} = \frac{7}{5}$

Step 2.5.2

Multiply $2$ by $5$ .

$\frac{2 y (3 + 10)}{5} - \frac{1}{2} = \frac{7}{5}$

Step 2.5.3

Add $3$ and $10$ .

$\frac{2 y \cdot 13}{5} - \frac{1}{2} = \frac{7}{5}$

Step 2.5.4

Multiply $13$ by $2$ .

$\frac{26 y}{5} - \frac{1}{2} = \frac{7}{5}$

Step 3

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

Tap for more steps...

Step 3.1

Add $\frac{1}{2}$ to both sides of the equation.

$\frac{26 y}{5} = \frac{7}{5} + \frac{1}{2}$

Step 3.2

To write $\frac{7}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{26 y}{5} = \frac{7}{5} \cdot \frac{2}{2} + \frac{1}{2}$

Step 3.3

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{26 y}{5} = \frac{7}{5} \cdot \frac{2}{2} + \frac{1}{2} \cdot \frac{5}{5}$

Step 3.4

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.4.1

Multiply $\frac{7}{5}$ by $\frac{2}{2}$ .

$\frac{26 y}{5} = \frac{7 \cdot 2}{5 \cdot 2} + \frac{1}{2} \cdot \frac{5}{5}$

Step 3.4.2

Multiply $5$ by $2$ .

$\frac{26 y}{5} = \frac{7 \cdot 2}{10} + \frac{1}{2} \cdot \frac{5}{5}$

Step 3.4.3

Multiply $\frac{1}{2}$ by $\frac{5}{5}$ .

$\frac{26 y}{5} = \frac{7 \cdot 2}{10} + \frac{5}{2 \cdot 5}$

Step 3.4.4

Multiply $2$ by $5$ .

$\frac{26 y}{5} = \frac{7 \cdot 2}{10} + \frac{5}{10}$

Step 3.5

Combine the numerators over the common denominator.

$\frac{26 y}{5} = \frac{7 \cdot 2 + 5}{10}$

Step 3.6

Simplify the numerator.

Tap for more steps...

Step 3.6.1

Multiply $7$ by $2$ .

$\frac{26 y}{5} = \frac{14 + 5}{10}$

Step 3.6.2

Add $14$ and $5$ .

$\frac{26 y}{5} = \frac{19}{10}$

Step 4

Multiply both sides of the equation by $\frac{5}{26}$ .

$\frac{5}{26} \cdot \frac{26 y}{5} = \frac{5}{26} \cdot \frac{19}{10}$

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 $\frac{5}{26} \cdot \frac{26 y}{5}$ .

Tap for more steps...

Step 5.1.1.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 5.1.1.1.1

Cancel the common factor.

$\frac{5}{26} \cdot \frac{26 y}{5} = \frac{5}{26} \cdot \frac{19}{10}$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{26} (26 y) = \frac{5}{26} \cdot \frac{19}{10}$

Step 5.1.1.2

Cancel the common factor of $26$ .

Tap for more steps...

Step 5.1.1.2.1

Factor $26$ out of $26 y$ .

$\frac{1}{26} (26 (y)) = \frac{5}{26} \cdot \frac{19}{10}$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{26} (26 y) = \frac{5}{26} \cdot \frac{19}{10}$

Step 5.1.1.2.3

Rewrite the expression.

$y = \frac{5}{26} \cdot \frac{19}{10}$

Step 5.2

Simplify the right side.

Tap for more steps...

Step 5.2.1

Simplify $\frac{5}{26} \cdot \frac{19}{10}$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 5.2.1.1.1

Factor $5$ out of $10$ .

$y = \frac{5}{26} \cdot \frac{19}{5 (2)}$

Step 5.2.1.1.2

Cancel the common factor.

$y = \frac{5}{26} \cdot \frac{19}{5 \cdot 2}$

Step 5.2.1.1.3

Rewrite the expression.

$y = \frac{1}{26} \cdot \frac{19}{2}$

Step 5.2.1.2

Multiply $\frac{1}{26}$ by $\frac{19}{2}$ .

$y = \frac{19}{26 \cdot 2}$

Step 5.2.1.3

Multiply $26$ by $2$ .

$y = \frac{19}{52}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = \frac{19}{52}$

Decimal Form:

$y = 0.36538461 \dots$