Finite Math Examples

$\frac{- 5 y - 8}{2} + 3 = - 5$

Step 1

Simplify $\frac{- 5 y - 8}{2} + 3$ .

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Step 1.1

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

$\frac{- 5 y - 8}{2} + 3 \cdot \frac{2}{2} = - 5$

Step 1.2

Simplify terms.

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Step 1.2.1

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

$\frac{- 5 y - 8}{2} + \frac{3 \cdot 2}{2} = - 5$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{- 5 y - 8 + 3 \cdot 2}{2} = - 5$

Step 1.3

Simplify the numerator.

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Step 1.3.1

Multiply $3$ by $2$ .

$\frac{- 5 y - 8 + 6}{2} = - 5$

Step 1.3.2

Add $- 8$ and $6$ .

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

Step 1.4

Simplify with factoring out.

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Step 1.4.1

Factor $- 1$ out of $- 5 y$ .

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

Step 1.4.2

Rewrite $- 2$ as $- 1 (2)$ .

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

Step 1.4.3

Factor $- 1$ out of $- (5 y) - 1 (2)$ .

$\frac{- (5 y + 2)}{2} = - 5$

Step 1.4.4

Simplify the expression.

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Step 1.4.4.1

Rewrite $- (5 y + 2)$ as $- 1 (5 y + 2)$ .

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

Step 1.4.4.2

Move the negative in front of the fraction.

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

Step 2

Multiply both sides of the equation by $- 2$ .

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

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $- 2 (- \frac{5 y + 2}{2})$ .

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Step 3.1.1.1

Cancel the common factor of $2$ .

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Step 3.1.1.1.1

Move the leading negative in $- \frac{5 y + 2}{2}$ into the numerator.

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

Step 3.1.1.1.2

Factor $2$ out of $- 2$ .

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

Step 3.1.1.1.3

Cancel the common factor.

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

Step 3.1.1.1.4

Rewrite the expression.

$- - (5 y + 2) = - 2 \cdot - 5$

Step 3.1.1.2

Multiply.

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Step 3.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 (5 y + 2) = - 2 \cdot - 5$

Step 3.1.1.2.2

Multiply $5 y + 2$ by $1$ .

$5 y + 2 = - 2 \cdot - 5$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $- 2$ by $- 5$ .

$5 y + 2 = 10$

Step 4

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

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Step 4.1

Subtract $2$ from both sides of the equation.

$5 y = 10 - 2$

Step 4.2

Subtract $2$ from $10$ .

$5 y = 8$

Step 5

Divide each term in $5 y = 8$ by $5$ and simplify.

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Step 5.1

Divide each term in $5 y = 8$ by $5$ .

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

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $5$ .

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Step 5.2.1.1

Cancel the common factor.

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

Step 5.2.1.2

Divide $y$ by $1$ .

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$y = 1.6$

Mixed Number Form:

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