Pre-Algebra Examples

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

Step 1

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

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Step 1.1

Subtract $8 y$ from both sides of the equation.

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

Step 1.2

Subtract $8 y$ from $4 y$ .

$2 - 4 y = - \frac{2}{5}$

Step 2

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

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Step 2.1

Subtract $2$ from both sides of the equation.

$- 4 y = - \frac{2}{5} - 2$

Step 2.2

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- 4 y = - \frac{2}{5} - 2 \cdot \frac{5}{5}$

Step 2.3

Combine $- 2$ and $\frac{5}{5}$ .

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

Step 2.4

Combine the numerators over the common denominator.

$- 4 y = \frac{- 2 - 2 \cdot 5}{5}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 2$ by $5$ .

$- 4 y = \frac{- 2 - 10}{5}$

Step 2.5.2

Subtract $10$ from $- 2$ .

$- 4 y = \frac{- 12}{5}$

Step 2.6

Move the negative in front of the fraction.

$- 4 y = - \frac{12}{5}$

Step 3

Divide each term in $- 4 y = - \frac{12}{5}$ by $- 4$ and simplify.

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Step 3.1

Divide each term in $- 4 y = - \frac{12}{5}$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{- \frac{12}{5}}{- 4}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 4$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{- \frac{12}{5}}{- 4}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- \frac{12}{5}}{- 4}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply the numerator by the reciprocal of the denominator.

$y = - \frac{12}{5} \cdot \frac{1}{- 4}$

Step 3.3.2

Cancel the common factor of $4$ .

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Step 3.3.2.1

Move the leading negative in $- \frac{12}{5}$ into the numerator.

$y = \frac{- 12}{5} \cdot \frac{1}{- 4}$

Step 3.3.2.2

Factor $4$ out of $- 12$ .

$y = \frac{4 (- 3)}{5} \cdot \frac{1}{- 4}$

Step 3.3.2.3

Factor $4$ out of $- 4$ .

$y = \frac{4 \cdot - 3}{5} \cdot \frac{1}{4 \cdot - 1}$

Step 3.3.2.4

Cancel the common factor.

$y = \frac{4 \cdot - 3}{5} \cdot \frac{1}{4 \cdot - 1}$

Step 3.3.2.5

Rewrite the expression.

$y = \frac{- 3}{5} \cdot \frac{1}{- 1}$

Step 3.3.3

Multiply $\frac{- 3}{5}$ by $\frac{1}{- 1}$ .

$y = \frac{- 3}{5 \cdot - 1}$

Step 3.3.4

Multiply $5$ by $- 1$ .

$y = \frac{- 3}{- 5}$

Step 3.3.5

Dividing two negative values results in a positive value.

$y = \frac{3}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{3}{5}$

Decimal Form:

$y = 0.6$