Pre-Algebra Examples

$2 (y + 1) - 3 (y - 1) = 5 y + 56 y$

Step 1

Simplify $2 (y + 1) - 3 (y - 1)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$2 y + 2 \cdot 1 - 3 (y - 1) = 5 y + 56 y$

Step 1.1.2

Multiply $2$ by $1$ .

$2 y + 2 - 3 (y - 1) = 5 y + 56 y$

Step 1.1.3

Apply the distributive property.

$2 y + 2 - 3 y - 3 \cdot - 1 = 5 y + 56 y$

Step 1.1.4

Multiply $- 3$ by $- 1$ .

$2 y + 2 - 3 y + 3 = 5 y + 56 y$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Subtract $3 y$ from $2 y$ .

$- y + 2 + 3 = 5 y + 56 y$

Step 1.2.2

Add $2$ and $3$ .

$- y + 5 = 5 y + 56 y$

Step 2

Add $5 y$ and $56 y$ .

$- y + 5 = 61 y$

Step 3

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

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Step 3.1

Subtract $61 y$ from both sides of the equation.

$- y + 5 - 61 y = 0$

Step 3.2

Subtract $61 y$ from $- y$ .

$- 62 y + 5 = 0$

Step 4

Subtract $5$ from both sides of the equation.

$- 62 y = - 5$

Step 5

Divide each term in $- 62 y = - 5$ by $- 62$ and simplify.

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Step 5.1

Divide each term in $- 62 y = - 5$ by $- 62$ .

$\frac{- 62 y}{- 62} = \frac{- 5}{- 62}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 62$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 62 y}{- 62} = \frac{- 5}{- 62}$

Step 5.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 5}{- 62}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Dividing two negative values results in a positive value.

$y = \frac{5}{62}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = \frac{5}{62}$

Decimal Form:

$y = 0.08064516 \dots$