Algebra Examples

$2 (6 y + 1) + 13 = 51 + 9 (y - 5)$

Step 1

Simplify $2 (6 y + 1) + 13$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$2 (6 y) + 2 \cdot 1 + 13 = 51 + 9 (y - 5)$

Step 1.1.2

Multiply $6$ by $2$ .

$12 y + 2 \cdot 1 + 13 = 51 + 9 (y - 5)$

Step 1.1.3

Multiply $2$ by $1$ .

$12 y + 2 + 13 = 51 + 9 (y - 5)$

Step 1.2

Add $2$ and $13$ .

$12 y + 15 = 51 + 9 (y - 5)$

Step 2

Simplify $51 + 9 (y - 5)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$12 y + 15 = 51 + 9 y + 9 \cdot - 5$

Step 2.1.2

Multiply $9$ by $- 5$ .

$12 y + 15 = 51 + 9 y - 45$

Step 2.2

Subtract $45$ from $51$ .

$12 y + 15 = 9 y + 6$

Step 3

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

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Step 3.1

Subtract $9 y$ from both sides of the equation.

$12 y + 15 - 9 y = 6$

Step 3.2

Subtract $9 y$ from $12 y$ .

$3 y + 15 = 6$

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.

$3 y = 6 - 15$

Step 4.2

Subtract $15$ from $6$ .

$3 y = - 9$

Step 5

Divide each term in $3 y = - 9$ by $3$ and simplify.

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Step 5.1

Divide each term in $3 y = - 9$ by $3$ .

$\frac{3 y}{3} = \frac{- 9}{3}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $3$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 9}{3}$

Step 5.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 9}{3}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $- 9$ by $3$ .

$y = - 3$