Basic Math Examples

$\frac{2 y - 2}{4} - \frac{5}{8} = \frac{- 9 y + 4}{8}$

Step 1

Multiply both sides by $8$ .

$(\frac{2 y - 2}{4} - \frac{5}{8}) \cdot 8 = \frac{- 9 y + 4}{8} \cdot 8$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{2 y - 2}{4} - \frac{5}{8}) \cdot 8$ .

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Step 2.1.1.1

Cancel the common factor of $2 y - 2$ and $4$ .

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Step 2.1.1.1.1

Factor $2$ out of $2 y$ .

$(\frac{2 (y) - 2}{4} - \frac{5}{8}) \cdot 8 = \frac{- 9 y + 4}{8} \cdot 8$

Step 2.1.1.1.2

Factor $2$ out of $- 2$ .

$(\frac{2 (y) + 2 (- 1)}{4} - \frac{5}{8}) \cdot 8 = \frac{- 9 y + 4}{8} \cdot 8$

Step 2.1.1.1.3

Factor $2$ out of $2 (y) + 2 (- 1)$ .

$(\frac{2 (y - 1)}{4} - \frac{5}{8}) \cdot 8 = \frac{- 9 y + 4}{8} \cdot 8$

Step 2.1.1.1.4

Cancel the common factors.

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Step 2.1.1.1.4.1

Factor $2$ out of $4$ .

$(\frac{2 (y - 1)}{2 (2)} - \frac{5}{8}) \cdot 8 = \frac{- 9 y + 4}{8} \cdot 8$

Step 2.1.1.1.4.2

Cancel the common factor.

$(\frac{2 (y - 1)}{2 \cdot 2} - \frac{5}{8}) \cdot 8 = \frac{- 9 y + 4}{8} \cdot 8$

Step 2.1.1.1.4.3

Rewrite the expression.

$(\frac{y - 1}{2} - \frac{5}{8}) \cdot 8 = \frac{- 9 y + 4}{8} \cdot 8$

Step 2.1.1.2

To write $\frac{y - 1}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(\frac{y - 1}{2} \cdot \frac{4}{4} - \frac{5}{8}) \cdot 8 = \frac{- 9 y + 4}{8} \cdot 8$

Step 2.1.1.3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1.1.3.1

Multiply $\frac{y - 1}{2}$ by $\frac{4}{4}$ .

$(\frac{(y - 1) \cdot 4}{2 \cdot 4} - \frac{5}{8}) \cdot 8 = \frac{- 9 y + 4}{8} \cdot 8$

Step 2.1.1.3.2

Multiply $2$ by $4$ .

$(\frac{(y - 1) \cdot 4}{8} - \frac{5}{8}) \cdot 8 = \frac{- 9 y + 4}{8} \cdot 8$

Step 2.1.1.4

Combine the numerators over the common denominator.

$\frac{(y - 1) \cdot 4 - 5}{8} \cdot 8 = \frac{- 9 y + 4}{8} \cdot 8$

Step 2.1.1.5

Simplify the numerator.

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Step 2.1.1.5.1

Apply the distributive property.

$\frac{y \cdot 4 - 1 \cdot 4 - 5}{8} \cdot 8 = \frac{- 9 y + 4}{8} \cdot 8$

Step 2.1.1.5.2

Move $4$ to the left of $y$ .

$\frac{4 \cdot y - 1 \cdot 4 - 5}{8} \cdot 8 = \frac{- 9 y + 4}{8} \cdot 8$

Step 2.1.1.5.3

Multiply $- 1$ by $4$ .

$\frac{4 \cdot y - 4 - 5}{8} \cdot 8 = \frac{- 9 y + 4}{8} \cdot 8$

Step 2.1.1.5.4

Subtract $5$ from $- 4$ .

$\frac{4 y - 9}{8} \cdot 8 = \frac{- 9 y + 4}{8} \cdot 8$

Step 2.1.1.6

Cancel the common factor of $8$ .

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Step 2.1.1.6.1

Cancel the common factor.

$\frac{4 y - 9}{8} \cdot 8 = \frac{- 9 y + 4}{8} \cdot 8$

Step 2.1.1.6.2

Rewrite the expression.

$4 y - 9 = \frac{- 9 y + 4}{8} \cdot 8$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $8$ .

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Step 2.2.1.1

Cancel the common factor.

$4 y - 9 = \frac{- 9 y + 4}{8} \cdot 8$

Step 2.2.1.2

Rewrite the expression.

$4 y - 9 = - 9 y + 4$

Step 3

Solve for $y$ .

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Step 3.1

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

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Step 3.1.1

Add $9 y$ to both sides of the equation.

$4 y - 9 + 9 y = 4$

Step 3.1.2

Add $4 y$ and $9 y$ .

$13 y - 9 = 4$

Step 3.2

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

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Step 3.2.1

Add $9$ to both sides of the equation.

$13 y = 4 + 9$

Step 3.2.2

Add $4$ and $9$ .

$13 y = 13$

Step 3.3

Divide each term in $13 y = 13$ by $13$ and simplify.

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Step 3.3.1

Divide each term in $13 y = 13$ by $13$ .

$\frac{13 y}{13} = \frac{13}{13}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $13$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{13 y}{13} = \frac{13}{13}$

Step 3.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{13}{13}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $13$ by $13$ .

$y = 1$