Pre-Algebra Examples

$\frac{y - 8}{6} + \frac{2 y - 2}{7} = 2$

Step 1

Simplify $\frac{y - 8}{6} + \frac{2 y - 2}{7}$ .

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Step 1.1

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

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Step 1.1.1

Factor $2$ out of $2 y$ .

$\frac{y - 8}{6} + \frac{2 (y) - 2}{7} = 2$

Step 1.1.2

Factor $2$ out of $- 2$ .

$\frac{y - 8}{6} + \frac{2 (y) + 2 (- 1)}{7} = 2$

Step 1.1.3

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

$\frac{y - 8}{6} + \frac{2 (y - 1)}{7} = 2$

Step 1.2

To write $\frac{y - 8}{6}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{y - 8}{6} \cdot \frac{7}{7} + \frac{2 (y - 1)}{7} = 2$

Step 1.3

To write $\frac{2 (y - 1)}{7}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{y - 8}{6} \cdot \frac{7}{7} + \frac{2 (y - 1)}{7} \cdot \frac{6}{6} = 2$

Step 1.4

Write each expression with a common denominator of $42$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{y - 8}{6}$ by $\frac{7}{7}$ .

$\frac{(y - 8) \cdot 7}{6 \cdot 7} + \frac{2 (y - 1)}{7} \cdot \frac{6}{6} = 2$

Step 1.4.2

Multiply $6$ by $7$ .

$\frac{(y - 8) \cdot 7}{42} + \frac{2 (y - 1)}{7} \cdot \frac{6}{6} = 2$

Step 1.4.3

Multiply $\frac{2 (y - 1)}{7}$ by $\frac{6}{6}$ .

$\frac{(y - 8) \cdot 7}{42} + \frac{2 (y - 1) \cdot 6}{7 \cdot 6} = 2$

Step 1.4.4

Multiply $7$ by $6$ .

$\frac{(y - 8) \cdot 7}{42} + \frac{2 (y - 1) \cdot 6}{42} = 2$

Step 1.5

Combine the numerators over the common denominator.

$\frac{(y - 8) \cdot 7 + 2 (y - 1) \cdot 6}{42} = 2$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Apply the distributive property.

$\frac{y \cdot 7 - 8 \cdot 7 + 2 (y - 1) \cdot 6}{42} = 2$

Step 1.6.2

Move $7$ to the left of $y$ .

$\frac{7 \cdot y - 8 \cdot 7 + 2 (y - 1) \cdot 6}{42} = 2$

Step 1.6.3

Multiply $- 8$ by $7$ .

$\frac{7 \cdot y - 56 + 2 (y - 1) \cdot 6}{42} = 2$

Step 1.6.4

Apply the distributive property.

$\frac{7 y - 56 + (2 y + 2 \cdot - 1) \cdot 6}{42} = 2$

Step 1.6.5

Multiply $2$ by $- 1$ .

$\frac{7 y - 56 + (2 y - 2) \cdot 6}{42} = 2$

Step 1.6.6

Apply the distributive property.

$\frac{7 y - 56 + 2 y \cdot 6 - 2 \cdot 6}{42} = 2$

Step 1.6.7

Multiply $6$ by $2$ .

$\frac{7 y - 56 + 12 y - 2 \cdot 6}{42} = 2$

Step 1.6.8

Multiply $- 2$ by $6$ .

$\frac{7 y - 56 + 12 y - 12}{42} = 2$

Step 1.6.9

Add $7 y$ and $12 y$ .

$\frac{19 y - 56 - 12}{42} = 2$

Step 1.6.10

Subtract $12$ from $- 56$ .

$\frac{19 y - 68}{42} = 2$

Step 2

Multiply both sides by $42$ .

$\frac{19 y - 68}{42} \cdot 42 = 2 \cdot 42$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $42$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{19 y - 68}{42} \cdot 42 = 2 \cdot 42$

Step 3.1.1.2

Rewrite the expression.

$19 y - 68 = 2 \cdot 42$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $2$ by $42$ .

$19 y - 68 = 84$

Step 4

Solve for $y$ .

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Step 4.1

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

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Step 4.1.1

Add $68$ to both sides of the equation.

$19 y = 84 + 68$

Step 4.1.2

Add $84$ and $68$ .

$19 y = 152$

Step 4.2

Divide each term in $19 y = 152$ by $19$ and simplify.

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Step 4.2.1

Divide each term in $19 y = 152$ by $19$ .

$\frac{19 y}{19} = \frac{152}{19}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $19$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{19 y}{19} = \frac{152}{19}$

Step 4.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{152}{19}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $152$ by $19$ .

$y = 8$