Finite Math Examples

$4 (y + 2) = 5 (y - 8)$

Step 1

Simplify $4 (y + 2)$ .

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Step 1.1

Rewrite.

$0 + 0 + 4 (y + 2) = 5 (y - 8)$

Step 1.2

Simplify by adding zeros.

$4 (y + 2) = 5 (y - 8)$

Step 1.3

Apply the distributive property.

$4 y + 4 \cdot 2 = 5 (y - 8)$

Step 1.4

Multiply $4$ by $2$ .

$4 y + 8 = 5 (y - 8)$

Step 2

Simplify $5 (y - 8)$ .

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Step 2.1

Apply the distributive property.

$4 y + 8 = 5 y + 5 \cdot - 8$

Step 2.2

Multiply $5$ by $- 8$ .

$4 y + 8 = 5 y - 40$

Step 3

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

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Step 3.1

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

$4 y + 8 - 5 y = - 40$

Step 3.2

Subtract $5 y$ from $4 y$ .

$- y + 8 = - 40$

Step 4

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

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Step 4.1

Subtract $8$ from both sides of the equation.

$- y = - 40 - 8$

Step 4.2

Subtract $8$ from $- 40$ .

$- y = - 48$

Step 5

Divide each term in $- y = - 48$ by $- 1$ and simplify.

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Step 5.1

Divide each term in $- y = - 48$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 48}{- 1}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 48}{- 1}$

Step 5.2.2

Divide $y$ by $1$ .

$y = \frac{- 48}{- 1}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $- 48$ by $- 1$ .

$y = 48$