Basic Math Examples

$(y - 8) = \frac{2}{3} \cdot (y - 7)$

Step 1

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

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Step 1.1

Rewrite.

$y - 8 = 0 + 0 + \frac{2}{3} \cdot (y - 7)$

Step 1.2

Simplify by adding zeros.

$y - 8 = \frac{2}{3} \cdot (y - 7)$

Step 1.3

Apply the distributive property.

$y - 8 = \frac{2}{3} y + \frac{2}{3} \cdot - 7$

Step 1.4

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

$y - 8 = \frac{2 y}{3} + \frac{2}{3} \cdot - 7$

Step 1.5

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

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Step 1.5.1

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

$y - 8 = \frac{2 y}{3} + \frac{2 \cdot - 7}{3}$

Step 1.5.2

Multiply $2$ by $- 7$ .

$y - 8 = \frac{2 y}{3} + \frac{- 14}{3}$

Step 1.6

Move the negative in front of the fraction.

$y - 8 = \frac{2 y}{3} - \frac{14}{3}$

Step 2

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

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Step 2.1

Subtract $\frac{2 y}{3}$ from both sides of the equation.

$y - 8 - \frac{2 y}{3} = - \frac{14}{3}$

Step 2.2

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

$y \cdot \frac{3}{3} - \frac{2 y}{3} - 8 = - \frac{14}{3}$

Step 2.3

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

$\frac{y \cdot 3}{3} - \frac{2 y}{3} - 8 = - \frac{14}{3}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{y \cdot 3 - 2 y}{3} - 8 = - \frac{14}{3}$

Step 2.5

Subtract $2 y$ from $y \cdot 3$ .

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Step 2.5.1

Reorder $y$ and $3$ .

$\frac{3 \cdot y - 2 y}{3} - 8 = - \frac{14}{3}$

Step 2.5.2

Subtract $2 y$ from $3 \cdot y$ .

$\frac{y}{3} - 8 = - \frac{14}{3}$

Step 3

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

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Step 3.1

Add $8$ to both sides of the equation.

$\frac{y}{3} = - \frac{14}{3} + 8$

Step 3.2

To write $8$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{y}{3} = - \frac{14}{3} + 8 \cdot \frac{3}{3}$

Step 3.3

Combine $8$ and $\frac{3}{3}$ .

$\frac{y}{3} = - \frac{14}{3} + \frac{8 \cdot 3}{3}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{y}{3} = \frac{- 14 + 8 \cdot 3}{3}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $8$ by $3$ .

$\frac{y}{3} = \frac{- 14 + 24}{3}$

Step 3.5.2

Add $- 14$ and $24$ .

$\frac{y}{3} = \frac{10}{3}$

Step 4

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$y = 10$