Basic Math Examples

$2 \cdot y + 6 = 3 - \frac{1}{5}$

Step 1

Simplify $3 - \frac{1}{5}$ .

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Step 1.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$2 y + 6 = 3 \cdot \frac{5}{5} - \frac{1}{5}$

Step 1.2

Combine $3$ and $\frac{5}{5}$ .

$2 y + 6 = \frac{3 \cdot 5}{5} - \frac{1}{5}$

Step 1.3

Combine the numerators over the common denominator.

$2 y + 6 = \frac{3 \cdot 5 - 1}{5}$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Multiply $3$ by $5$ .

$2 y + 6 = \frac{15 - 1}{5}$

Step 1.4.2

Subtract $1$ from $15$ .

$2 y + 6 = \frac{14}{5}$

Step 2

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

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Step 2.1

Subtract $6$ from both sides of the equation.

$2 y = \frac{14}{5} - 6$

Step 2.2

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$2 y = \frac{14}{5} - 6 \cdot \frac{5}{5}$

Step 2.3

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

$2 y = \frac{14}{5} + \frac{- 6 \cdot 5}{5}$

Step 2.4

Combine the numerators over the common denominator.

$2 y = \frac{14 - 6 \cdot 5}{5}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 6$ by $5$ .

$2 y = \frac{14 - 30}{5}$

Step 2.5.2

Subtract $30$ from $14$ .

$2 y = \frac{- 16}{5}$

Step 2.6

Move the negative in front of the fraction.

$2 y = - \frac{16}{5}$

Step 3

Divide each term in $2 y = - \frac{16}{5}$ by $2$ and simplify.

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Step 3.1

Divide each term in $2 y = - \frac{16}{5}$ by $2$ .

$\frac{2 y}{2} = \frac{- \frac{16}{5}}{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{- \frac{16}{5}}{2}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- \frac{16}{5}}{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply the numerator by the reciprocal of the denominator.

$y = - \frac{16}{5} \cdot \frac{1}{2}$

Step 3.3.2

Cancel the common factor of $2$ .

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Step 3.3.2.1

Move the leading negative in $- \frac{16}{5}$ into the numerator.

$y = \frac{- 16}{5} \cdot \frac{1}{2}$

Step 3.3.2.2

Factor $2$ out of $- 16$ .

$y = \frac{2 (- 8)}{5} \cdot \frac{1}{2}$

Step 3.3.2.3

Cancel the common factor.

$y = \frac{2 \cdot - 8}{5} \cdot \frac{1}{2}$

Step 3.3.2.4

Rewrite the expression.

$y = \frac{- 8}{5}$

Step 3.3.3

Move the negative in front of the fraction.

$y = - \frac{8}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{8}{5}$

Decimal Form:

$y = - 1.6$

Mixed Number Form:

$y = - 1 \frac{3}{5}$