Finite Math Examples

$3 (4 y + 5) = 2 (5 y - 4)$

Step 1

Simplify $3 (4 y + 5)$ .

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Step 1.1

Rewrite.

$0 + 0 + 3 (4 y + 5) = 2 (5 y - 4)$

Step 1.2

Simplify by adding zeros.

$3 (4 y + 5) = 2 (5 y - 4)$

Step 1.3

Apply the distributive property.

$3 (4 y) + 3 \cdot 5 = 2 (5 y - 4)$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $4$ by $3$ .

$12 y + 3 \cdot 5 = 2 (5 y - 4)$

Step 1.4.2

Multiply $3$ by $5$ .

$12 y + 15 = 2 (5 y - 4)$

Step 2

Simplify $2 (5 y - 4)$ .

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Step 2.1

Apply the distributive property.

$12 y + 15 = 2 (5 y) + 2 \cdot - 4$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $5$ by $2$ .

$12 y + 15 = 10 y + 2 \cdot - 4$

Step 2.2.2

Multiply $2$ by $- 4$ .

$12 y + 15 = 10 y - 8$

Step 3

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

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Step 3.1

Subtract $10 y$ from both sides of the equation.

$12 y + 15 - 10 y = - 8$

Step 3.2

Subtract $10 y$ from $12 y$ .

$2 y + 15 = - 8$

Step 4

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

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Step 4.1

Subtract $15$ from both sides of the equation.

$2 y = - 8 - 15$

Step 4.2

Subtract $15$ from $- 8$ .

$2 y = - 23$

Step 5

Divide each term in $2 y = - 23$ by $2$ and simplify.

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Step 5.1

Divide each term in $2 y = - 23$ by $2$ .

$\frac{2 y}{2} = \frac{- 23}{2}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $2$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{- 23}{2}$

Step 5.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 23}{2}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Move the negative in front of the fraction.

$y = - \frac{23}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{23}{2}$

Decimal Form:

$y = - 11.5$

Mixed Number Form:

$y = - 11 \frac{1}{2}$