Algebra Examples

$- 4 y + 8 - 2 y = 8 (\frac{3}{4} y + 3 + \frac{1}{2} y)$

Step 1

Subtract $2 y$ from $- 4 y$ .

$- 6 y + 8 = 8 (\frac{3}{4} y + 3 + \frac{1}{2} y)$

Step 2

Simplify $8 (\frac{3}{4} y + 3 + \frac{1}{2} y)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Combine $\frac{3}{4}$ and $y$ .

$- 6 y + 8 = 8 (\frac{3 y}{4} + 3 + \frac{1}{2} y)$

Step 2.1.2

Combine $\frac{1}{2}$ and $y$ .

$- 6 y + 8 = 8 (\frac{3 y}{4} + 3 + \frac{y}{2})$

Step 2.2

To write $\frac{y}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 6 y + 8 = 8 (\frac{3 y}{4} + \frac{y}{2} \cdot \frac{2}{2} + 3)$

Step 2.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{y}{2}$ by $\frac{2}{2}$ .

$- 6 y + 8 = 8 (\frac{3 y}{4} + \frac{y \cdot 2}{2 \cdot 2} + 3)$

Step 2.3.2

Multiply $2$ by $2$ .

$- 6 y + 8 = 8 (\frac{3 y}{4} + \frac{y \cdot 2}{4} + 3)$

Step 2.4

Combine the numerators over the common denominator.

$- 6 y + 8 = 8 (\frac{3 y + y \cdot 2}{4} + 3)$

Step 2.5

Add $3 y$ and $y \cdot 2$ .

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Step 2.5.1

Reorder $y$ and $2$ .

$- 6 y + 8 = 8 (\frac{3 y + 2 \cdot y}{4} + 3)$

Step 2.5.2

Add $3 y$ and $2 \cdot y$ .

$- 6 y + 8 = 8 (\frac{5 y}{4} + 3)$

Step 2.6

Apply the distributive property.

$- 6 y + 8 = 8 \frac{5 y}{4} + 8 \cdot 3$

Step 2.7

Cancel the common factor of $4$ .

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Step 2.7.1

Factor $4$ out of $8$ .

$- 6 y + 8 = 4 (2) \frac{5 y}{4} + 8 \cdot 3$

Step 2.7.2

Cancel the common factor.

$- 6 y + 8 = 4 \cdot 2 \frac{5 y}{4} + 8 \cdot 3$

Step 2.7.3

Rewrite the expression.

$- 6 y + 8 = 2 (5 y) + 8 \cdot 3$

Step 2.8

Multiply.

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Step 2.8.1

Multiply $5$ by $2$ .

$- 6 y + 8 = 10 y + 8 \cdot 3$

Step 2.8.2

Multiply $8$ by $3$ .

$- 6 y + 8 = 10 y + 24$

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.

$- 6 y + 8 - 10 y = 24$

Step 3.2

Subtract $10 y$ from $- 6 y$ .

$- 16 y + 8 = 24$

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.

$- 16 y = 24 - 8$

Step 4.2

Subtract $8$ from $24$ .

$- 16 y = 16$

Step 5

Divide each term in $- 16 y = 16$ by $- 16$ and simplify.

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Step 5.1

Divide each term in $- 16 y = 16$ by $- 16$ .

$\frac{- 16 y}{- 16} = \frac{16}{- 16}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 16$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 16 y}{- 16} = \frac{16}{- 16}$

Step 5.2.1.2

Divide $y$ by $1$ .

$y = \frac{16}{- 16}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $16$ by $- 16$ .

$y = - 1$