Basic Math Examples

$\frac{4 (y - 2)}{2} = \frac{4 (y + 2)}{10}$

Step 1

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

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Step 1.1

Factor $2$ out of $4 (y - 2)$ .

$\frac{2 (2 (y - 2))}{2} = \frac{4 (y + 2)}{10}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $2$ .

$\frac{2 (2 (y - 2))}{2 (1)} = \frac{4 (y + 2)}{10}$

Step 1.2.2

Cancel the common factor.

$\frac{2 (2 (y - 2))}{2 \cdot 1} = \frac{4 (y + 2)}{10}$

Step 1.2.3

Rewrite the expression.

$\frac{2 (y - 2)}{1} = \frac{4 (y + 2)}{10}$

Step 1.2.4

Divide $2 (y - 2)$ by $1$ .

$2 (y - 2) = \frac{4 (y + 2)}{10}$

Step 2

Solve for $y$ .

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Step 2.1

Cancel the common factor of $4$ and $10$ .

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Step 2.1.1

Factor $2$ out of $4 (y + 2)$ .

$2 (y - 2) = \frac{2 (2 (y + 2))}{10}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $2$ out of $10$ .

$2 (y - 2) = \frac{2 (2 (y + 2))}{2 (5)}$

Step 2.1.2.2

Cancel the common factor.

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

Step 2.1.2.3

Rewrite the expression.

$2 (y - 2) = \frac{2 (y + 2)}{5}$

Step 2.2

Multiply both sides by $5$ .

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

Step 2.3

Simplify.

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Step 2.3.1

Simplify the left side.

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Step 2.3.1.1

Simplify $2 (y - 2) \cdot 5$ .

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Step 2.3.1.1.1

Apply the distributive property.

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

Step 2.3.1.1.2

Multiply $2$ by $- 2$ .

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

Step 2.3.1.1.3

Apply the distributive property.

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

Step 2.3.1.1.4

Multiply.

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Step 2.3.1.1.4.1

Multiply $5$ by $2$ .

$10 y - 4 \cdot 5 = \frac{2 (y + 2)}{5} \cdot 5$

Step 2.3.1.1.4.2

Multiply $- 4$ by $5$ .

$10 y - 20 = \frac{2 (y + 2)}{5} \cdot 5$

Step 2.3.2

Simplify the right side.

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Step 2.3.2.1

Simplify $\frac{2 (y + 2)}{5} \cdot 5$ .

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Step 2.3.2.1.1

Cancel the common factor of $5$ .

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Step 2.3.2.1.1.1

Cancel the common factor.

$10 y - 20 = \frac{2 (y + 2)}{5} \cdot 5$

Step 2.3.2.1.1.2

Rewrite the expression.

$10 y - 20 = 2 (y + 2)$

Step 2.3.2.1.2

Apply the distributive property.

$10 y - 20 = 2 y + 2 \cdot 2$

Step 2.3.2.1.3

Multiply $2$ by $2$ .

$10 y - 20 = 2 y + 4$

Step 2.4

Solve for $y$ .

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Step 2.4.1

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

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Step 2.4.1.1

Subtract $2 y$ from both sides of the equation.

$10 y - 20 - 2 y = 4$

Step 2.4.1.2

Subtract $2 y$ from $10 y$ .

$8 y - 20 = 4$

Step 2.4.2

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

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Step 2.4.2.1

Add $20$ to both sides of the equation.

$8 y = 4 + 20$

Step 2.4.2.2

Add $4$ and $20$ .

$8 y = 24$

Step 2.4.3

Divide each term in $8 y = 24$ by $8$ and simplify.

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Step 2.4.3.1

Divide each term in $8 y = 24$ by $8$ .

$\frac{8 y}{8} = \frac{24}{8}$

Step 2.4.3.2

Simplify the left side.

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Step 2.4.3.2.1

Cancel the common factor of $8$ .

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Step 2.4.3.2.1.1

Cancel the common factor.

$\frac{8 y}{8} = \frac{24}{8}$

Step 2.4.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{24}{8}$

Step 2.4.3.3

Simplify the right side.

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Step 2.4.3.3.1

Divide $24$ by $8$ .

$y = 3$