Basic Math Examples

$20 - (1 + 7 y - 4 (y + 3)) = - 5 (3 y - 6) - (9 (y - 1) - 18 y + 20)$

Step 1

Since $y$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- 5 (3 y - 6) - (9 (y - 1) - 18 y + 20) = 20 - (1 + 7 y - 4 (y + 3))$

Step 2

Simplify $- 5 (3 y - 6) - (9 (y - 1) - 18 y + 20)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$- 5 (3 y) - 5 \cdot - 6 - (9 (y - 1) - 18 y + 20) = 20 - (1 + 7 y - 4 (y + 3))$

Step 2.1.2

Multiply $3$ by $- 5$ .

$- 15 y - 5 \cdot - 6 - (9 (y - 1) - 18 y + 20) = 20 - (1 + 7 y - 4 (y + 3))$

Step 2.1.3

Multiply $- 5$ by $- 6$ .

$- 15 y + 30 - (9 (y - 1) - 18 y + 20) = 20 - (1 + 7 y - 4 (y + 3))$

Step 2.1.4

Simplify each term.

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Step 2.1.4.1

Apply the distributive property.

$- 15 y + 30 - (9 y + 9 \cdot - 1 - 18 y + 20) = 20 - (1 + 7 y - 4 (y + 3))$

Step 2.1.4.2

Multiply $9$ by $- 1$ .

$- 15 y + 30 - (9 y - 9 - 18 y + 20) = 20 - (1 + 7 y - 4 (y + 3))$

Step 2.1.5

Subtract $18 y$ from $9 y$ .

$- 15 y + 30 - (- 9 y - 9 + 20) = 20 - (1 + 7 y - 4 (y + 3))$

Step 2.1.6

Add $- 9$ and $20$ .

$- 15 y + 30 - (- 9 y + 11) = 20 - (1 + 7 y - 4 (y + 3))$

Step 2.1.7

Apply the distributive property.

$- 15 y + 30 - (- 9 y) - 1 \cdot 11 = 20 - (1 + 7 y - 4 (y + 3))$

Step 2.1.8

Multiply $- 9$ by $- 1$ .

$- 15 y + 30 + 9 y - 1 \cdot 11 = 20 - (1 + 7 y - 4 (y + 3))$

Step 2.1.9

Multiply $- 1$ by $11$ .

$- 15 y + 30 + 9 y - 11 = 20 - (1 + 7 y - 4 (y + 3))$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Add $- 15 y$ and $9 y$ .

$- 6 y + 30 - 11 = 20 - (1 + 7 y - 4 (y + 3))$

Step 2.2.2

Subtract $11$ from $30$ .

$- 6 y + 19 = 20 - (1 + 7 y - 4 (y + 3))$

Step 3

Simplify $20 - (1 + 7 y - 4 (y + 3))$ .

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Step 3.1

Simplify each term.

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Step 3.1.1

Simplify each term.

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Step 3.1.1.1

Apply the distributive property.

$- 6 y + 19 = 20 - (1 + 7 y - 4 y - 4 \cdot 3)$

Step 3.1.1.2

Multiply $- 4$ by $3$ .

$- 6 y + 19 = 20 - (1 + 7 y - 4 y - 12)$

Step 3.1.2

Subtract $12$ from $1$ .

$- 6 y + 19 = 20 - (7 y - 4 y - 11)$

Step 3.1.3

Subtract $4 y$ from $7 y$ .

$- 6 y + 19 = 20 - (3 y - 11)$

Step 3.1.4

Apply the distributive property.

$- 6 y + 19 = 20 - (3 y) - - 11$

Step 3.1.5

Multiply $3$ by $- 1$ .

$- 6 y + 19 = 20 - 3 y - - 11$

Step 3.1.6

Multiply $- 1$ by $- 11$ .

$- 6 y + 19 = 20 - 3 y + 11$

Step 3.2

Add $20$ and $11$ .

$- 6 y + 19 = - 3 y + 31$

Step 4

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

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Step 4.1

Add $3 y$ to both sides of the equation.

$- 6 y + 19 + 3 y = 31$

Step 4.2

Add $- 6 y$ and $3 y$ .

$- 3 y + 19 = 31$

Step 5

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

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Step 5.1

Subtract $19$ from both sides of the equation.

$- 3 y = 31 - 19$

Step 5.2

Subtract $19$ from $31$ .

$- 3 y = 12$

Step 6

Divide each term in $- 3 y = 12$ by $- 3$ and simplify.

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Step 6.1

Divide each term in $- 3 y = 12$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{12}{- 3}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $- 3$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{12}{- 3}$

Step 6.2.1.2

Divide $y$ by $1$ .

$y = \frac{12}{- 3}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $12$ by $- 3$ .

$y = - 4$