Basic Math Examples

$- 2 (y + 4) = 8 y - 4 + 4 (2 y + 1)$

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.

$8 y - 4 + 4 (2 y + 1) = - 2 (y + 4)$

Step 2

Simplify $8 y - 4 + 4 (2 y + 1)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$8 y - 4 + 4 (2 y) + 4 \cdot 1 = - 2 (y + 4)$

Step 2.1.2

Multiply $2$ by $4$ .

$8 y - 4 + 8 y + 4 \cdot 1 = - 2 (y + 4)$

Step 2.1.3

Multiply $4$ by $1$ .

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

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Combine the opposite terms in $8 y - 4 + 8 y + 4$ .

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Step 2.2.1.1

Add $- 4$ and $4$ .

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

Step 2.2.1.2

Add $8 y + 8 y$ and $0$ .

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

Step 2.2.2

Add $8 y$ and $8 y$ .

$16 y = - 2 (y + 4)$

Step 3

Simplify $- 2 (y + 4)$ .

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Step 3.1

Apply the distributive property.

$16 y = - 2 y - 2 \cdot 4$

Step 3.2

Multiply $- 2$ by $4$ .

$16 y = - 2 y - 8$

Step 4

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

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Step 4.1

Add $2 y$ to both sides of the equation.

$16 y + 2 y = - 8$

Step 4.2

Add $16 y$ and $2 y$ .

$18 y = - 8$

Step 5

Divide each term in $18 y = - 8$ by $18$ and simplify.

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Step 5.1

Divide each term in $18 y = - 8$ by $18$ .

$\frac{18 y}{18} = \frac{- 8}{18}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $18$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{18 y}{18} = \frac{- 8}{18}$

Step 5.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 8}{18}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Cancel the common factor of $- 8$ and $18$ .

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Step 5.3.1.1

Factor $2$ out of $- 8$ .

$y = \frac{2 (- 4)}{18}$

Step 5.3.1.2

Cancel the common factors.

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Step 5.3.1.2.1

Factor $2$ out of $18$ .

$y = \frac{2 \cdot - 4}{2 \cdot 9}$

Step 5.3.1.2.2

Cancel the common factor.

$y = \frac{2 \cdot - 4}{2 \cdot 9}$

Step 5.3.1.2.3

Rewrite the expression.

$y = \frac{- 4}{9}$

Step 5.3.2

Move the negative in front of the fraction.

$y = - \frac{4}{9}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{4}{9}$

Decimal Form:

$y = - 0.\overline{4}$