Pre-Algebra Examples

$\frac{4}{7} y - 2 = \frac{3}{7} y + \frac{3}{14}$

Step 1

Combine $\frac{4}{7}$ and $y$ .

$\frac{4 y}{7} - 2 = \frac{3}{7} y + \frac{3}{14}$

Step 2

Combine $\frac{3}{7}$ and $y$ .

$\frac{4 y}{7} - 2 = \frac{3 y}{7} + \frac{3}{14}$

Step 3

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

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Step 3.1

Subtract $\frac{3 y}{7}$ from both sides of the equation.

$\frac{4 y}{7} - 2 - \frac{3 y}{7} = \frac{3}{14}$

Step 3.2

Combine the numerators over the common denominator.

$- 2 + \frac{4 y - 3 y}{7} = \frac{3}{14}$

Step 3.3

Subtract $3 y$ from $4 y$ .

$- 2 + \frac{y}{7} = \frac{3}{14}$

Step 4

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

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Step 4.1

Add $2$ to both sides of the equation.

$\frac{y}{7} = \frac{3}{14} + 2$

Step 4.2

To write $2$ as a fraction with a common denominator, multiply by $\frac{14}{14}$ .

$\frac{y}{7} = \frac{3}{14} + 2 \cdot \frac{14}{14}$

Step 4.3

Combine $2$ and $\frac{14}{14}$ .

$\frac{y}{7} = \frac{3}{14} + \frac{2 \cdot 14}{14}$

Step 4.4

Combine the numerators over the common denominator.

$\frac{y}{7} = \frac{3 + 2 \cdot 14}{14}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $2$ by $14$ .

$\frac{y}{7} = \frac{3 + 28}{14}$

Step 4.5.2

Add $3$ and $28$ .

$\frac{y}{7} = \frac{31}{14}$

Step 5

Multiply both sides of the equation by $7$ .

$7 \frac{y}{7} = 7 (\frac{31}{14})$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Cancel the common factor of $7$ .

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Step 6.1.1.1

Cancel the common factor.

$7 \frac{y}{7} = 7 (\frac{31}{14})$

Step 6.1.1.2

Rewrite the expression.

$y = 7 (\frac{31}{14})$

Step 6.2

Simplify the right side.

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Step 6.2.1

Cancel the common factor of $7$ .

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Step 6.2.1.1

Factor $7$ out of $14$ .

$y = 7 \frac{31}{7 (2)}$

Step 6.2.1.2

Cancel the common factor.

$y = 7 \frac{31}{7 \cdot 2}$

Step 6.2.1.3

Rewrite the expression.

$y = \frac{31}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$y = \frac{31}{2}$

Decimal Form:

$y = 15.5$

Mixed Number Form:

$y = 15 \frac{1}{2}$