Pre-Algebra Examples

$\frac{10}{4} y + \frac{8}{2} = 2 y - 2$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $2$ out of $10$ .

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

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $2$ out of $4$ .

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

Step 1.1.2.2

Cancel the common factor.

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

Step 1.1.2.3

Rewrite the expression.

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

Step 1.2

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

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

Step 1.3

Divide $8$ by $2$ .

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Simplify each term.

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Step 2.5.1

Simplify the numerator.

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Step 2.5.1.1

Factor $y$ out of $5 y - 2 y \cdot 2$ .

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Step 2.5.1.1.1

Factor $y$ out of $5 y$ .

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

Step 2.5.1.1.2

Factor $y$ out of $- 2 y \cdot 2$ .

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

Step 2.5.1.1.3

Factor $y$ out of $y \cdot 5 + y (- 2 \cdot 2)$ .

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

Step 2.5.1.2

Multiply $- 2$ by $2$ .

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

Step 2.5.1.3

Subtract $4$ from $5$ .

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

Step 2.5.2

Multiply $y$ by $1$ .

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

Step 3

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

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Step 3.1

Subtract $4$ from both sides of the equation.

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

Step 3.2

Subtract $4$ from $- 2$ .

$\frac{y}{2} = - 6$

Step 4

Multiply both sides of the equation by $2$ .

$2 \frac{y}{2} = 2 \cdot - 6$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $2$ .

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Step 5.1.1.1

Cancel the common factor.

$2 \frac{y}{2} = 2 \cdot - 6$

Step 5.1.1.2

Rewrite the expression.

$y = 2 \cdot - 6$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $2$ by $- 6$ .

$y = - 12$