Basic Math Examples

$\frac{2}{3} \cdot (y - 7) = \frac{3}{4} \cdot (4 y - 5)$

Step 1

Simplify $\frac{2}{3} \cdot (y - 7)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{2}{3} \cdot (y - 7) = \frac{3}{4} \cdot (4 y - 5)$

Step 1.2

Simplify by adding zeros.

$\frac{2}{3} \cdot (y - 7) = \frac{3}{4} \cdot (4 y - 5)$

Step 1.3

Apply the distributive property.

$\frac{2}{3} y + \frac{2}{3} \cdot - 7 = \frac{3}{4} \cdot (4 y - 5)$

Step 1.4

Combine $\frac{2}{3}$ and $y$ .

$\frac{2 y}{3} + \frac{2}{3} \cdot - 7 = \frac{3}{4} \cdot (4 y - 5)$

Step 1.5

Multiply $\frac{2}{3} \cdot - 7$ .

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Step 1.5.1

Combine $\frac{2}{3}$ and $- 7$ .

$\frac{2 y}{3} + \frac{2 \cdot - 7}{3} = \frac{3}{4} \cdot (4 y - 5)$

Step 1.5.2

Multiply $2$ by $- 7$ .

$\frac{2 y}{3} + \frac{- 14}{3} = \frac{3}{4} \cdot (4 y - 5)$

Step 1.6

Move the negative in front of the fraction.

$\frac{2 y}{3} - \frac{14}{3} = \frac{3}{4} \cdot (4 y - 5)$

Step 2

Simplify $\frac{3}{4} \cdot (4 y - 5)$ .

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Step 2.1

Apply the distributive property.

$\frac{2 y}{3} - \frac{14}{3} = \frac{3}{4} (4 y) + \frac{3}{4} \cdot - 5$

Step 2.2

Cancel the common factor of $4$ .

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Step 2.2.1

Factor $4$ out of $4 y$ .

$\frac{2 y}{3} - \frac{14}{3} = \frac{3}{4} (4 (y)) + \frac{3}{4} \cdot - 5$

Step 2.2.2

Cancel the common factor.

$\frac{2 y}{3} - \frac{14}{3} = \frac{3}{4} (4 y) + \frac{3}{4} \cdot - 5$

Step 2.2.3

Rewrite the expression.

$\frac{2 y}{3} - \frac{14}{3} = 3 y + \frac{3}{4} \cdot - 5$

Step 2.3

Multiply $\frac{3}{4} \cdot - 5$ .

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Step 2.3.1

Combine $\frac{3}{4}$ and $- 5$ .

$\frac{2 y}{3} - \frac{14}{3} = 3 y + \frac{3 \cdot - 5}{4}$

Step 2.3.2

Multiply $3$ by $- 5$ .

$\frac{2 y}{3} - \frac{14}{3} = 3 y + \frac{- 15}{4}$

Step 2.4

Move the negative in front of the fraction.

$\frac{2 y}{3} - \frac{14}{3} = 3 y - \frac{15}{4}$

Step 3

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

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Step 3.1

Subtract $3 y$ from both sides of the equation.

$\frac{2 y}{3} - \frac{14}{3} - 3 y = - \frac{15}{4}$

Step 3.2

To write $- 3 y$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 y}{3} - 3 y \cdot \frac{3}{3} - \frac{14}{3} = - \frac{15}{4}$

Step 3.3

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

$\frac{2 y}{3} + \frac{- 3 y \cdot 3}{3} - \frac{14}{3} = - \frac{15}{4}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{2 y - 3 y \cdot 3}{3} - \frac{14}{3} = - \frac{15}{4}$

Step 3.5

Combine the numerators over the common denominator.

$\frac{2 y - 3 y \cdot 3 - 14}{3} = - \frac{15}{4}$

Step 3.6

Multiply $3$ by $- 3$ .

$\frac{2 y - 9 y - 14}{3} = - \frac{15}{4}$

Step 3.7

Subtract $9 y$ from $2 y$ .

$\frac{- 7 y - 14}{3} = - \frac{15}{4}$

Step 3.8

Factor $7$ out of $- 7 y - 14$ .

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Step 3.8.1

Factor $7$ out of $- 7 y$ .

$\frac{7 (- y) - 14}{3} = - \frac{15}{4}$

Step 3.8.2

Factor $7$ out of $- 14$ .

$\frac{7 (- y) + 7 (- 2)}{3} = - \frac{15}{4}$

Step 3.8.3

Factor $7$ out of $7 (- y) + 7 (- 2)$ .

$\frac{7 (- y - 2)}{3} = - \frac{15}{4}$

Step 3.9

Factor $- 1$ out of $- y$ .

$\frac{7 (- (y) - 2)}{3} = - \frac{15}{4}$

Step 3.10

Rewrite $- 2$ as $- 1 (2)$ .

$\frac{7 (- (y) - 1 (2))}{3} = - \frac{15}{4}$

Step 3.11

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

$\frac{7 (- (y + 2))}{3} = - \frac{15}{4}$

Step 3.12

Rewrite $- (y + 2)$ as $- 1 (y + 2)$ .

$\frac{7 (- 1 (y + 2))}{3} = - \frac{15}{4}$

Step 3.13

Move the negative in front of the fraction.

$- \frac{7 (y + 2)}{3} = - \frac{15}{4}$

Step 4

Multiply both sides of the equation by $- \frac{3}{7}$ .

$- \frac{3}{7} (- \frac{7 (y + 2)}{3}) = - \frac{3}{7} (- \frac{15}{4})$

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

Simplify $- \frac{3}{7} (- \frac{7 (y + 2)}{3})$ .

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Step 5.1.1.1

Cancel the common factor of $3$ .

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Step 5.1.1.1.1

Move the leading negative in $- \frac{3}{7}$ into the numerator.

$\frac{- 3}{7} (- \frac{7 (y + 2)}{3}) = - \frac{3}{7} (- \frac{15}{4})$

Step 5.1.1.1.2

Move the leading negative in $- \frac{7 (y + 2)}{3}$ into the numerator.

$\frac{- 3}{7} \cdot \frac{- 7 (y + 2)}{3} = - \frac{3}{7} (- \frac{15}{4})$

Step 5.1.1.1.3

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{7} \cdot \frac{- 7 (y + 2)}{3} = - \frac{3}{7} (- \frac{15}{4})$

Step 5.1.1.1.4

Cancel the common factor.

$\frac{3 \cdot - 1}{7} \cdot \frac{- 7 (y + 2)}{3} = - \frac{3}{7} (- \frac{15}{4})$

Step 5.1.1.1.5

Rewrite the expression.

$\frac{- 1}{7} (- 7 (y + 2)) = - \frac{3}{7} (- \frac{15}{4})$

Step 5.1.1.2

Cancel the common factor of $7$ .

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Step 5.1.1.2.1

Factor $7$ out of $- 7 (y + 2)$ .

$\frac{- 1}{7} (7 (- (y + 2))) = - \frac{3}{7} (- \frac{15}{4})$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{- 1}{7} (7 (- (y + 2))) = - \frac{3}{7} (- \frac{15}{4})$

Step 5.1.1.2.3

Rewrite the expression.

$- - (y + 2) = - \frac{3}{7} (- \frac{15}{4})$

Step 5.1.1.3

Multiply.

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Step 5.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 (y + 2) = - \frac{3}{7} (- \frac{15}{4})$

Step 5.1.1.3.2

Multiply $y + 2$ by $1$ .

$y + 2 = - \frac{3}{7} (- \frac{15}{4})$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $- \frac{3}{7} (- \frac{15}{4})$ .

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Step 5.2.1.1

Multiply $- 1$ by $- 1$ .

$y + 2 = 1 (\frac{3}{7}) \frac{15}{4}$

Step 5.2.1.2

Multiply $\frac{3}{7}$ by $1$ .

$y + 2 = \frac{3}{7} \cdot \frac{15}{4}$

Step 5.2.1.3

Multiply $\frac{3}{7}$ by $\frac{15}{4}$ .

$y + 2 = \frac{3 \cdot 15}{7 \cdot 4}$

Step 5.2.1.4

Multiply $3$ by $15$ .

$y + 2 = \frac{45}{7 \cdot 4}$

Step 5.2.1.5

Multiply $7$ by $4$ .

$y + 2 = \frac{45}{28}$

Step 6

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

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Step 6.1

Subtract $2$ from both sides of the equation.

$y = \frac{45}{28} - 2$

Step 6.2

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{28}{28}$ .

$y = \frac{45}{28} - 2 \cdot \frac{28}{28}$

Step 6.3

Combine $- 2$ and $\frac{28}{28}$ .

$y = \frac{45}{28} + \frac{- 2 \cdot 28}{28}$

Step 6.4

Combine the numerators over the common denominator.

$y = \frac{45 - 2 \cdot 28}{28}$

Step 6.5

Simplify the numerator.

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Step 6.5.1

Multiply $- 2$ by $28$ .

$y = \frac{45 - 56}{28}$

Step 6.5.2

Subtract $56$ from $45$ .

$y = \frac{- 11}{28}$

Step 6.6

Move the negative in front of the fraction.

$y = - \frac{11}{28}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{11}{28}$

Decimal Form:

$y = - 0.39285714 \dots$