Finite Math Examples

$10 - \frac{2}{3} y = 4$

Step 1

Simplify each term.

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Step 1.1

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

$10 - \frac{y \cdot 2}{3} = 4$

Step 1.2

Move $2$ to the left of $y$ .

$10 - \frac{2 y}{3} = 4$

Step 2

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

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Step 2.1

Subtract $10$ from both sides of the equation.

$- \frac{2 y}{3} = 4 - 10$

Step 2.2

Subtract $10$ from $4$ .

$- \frac{2 y}{3} = - 6$

Step 3

Multiply both sides of the equation by $- \frac{3}{2}$ .

$- \frac{3}{2} (- \frac{2 y}{3}) = - \frac{3}{2} \cdot - 6$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

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

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Step 4.1.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$\frac{- 3}{2} (- \frac{2 y}{3}) = - \frac{3}{2} \cdot - 6$

Step 4.1.1.1.2

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

$\frac{- 3}{2} \cdot \frac{- 2 y}{3} = - \frac{3}{2} \cdot - 6$

Step 4.1.1.1.3

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{2} \cdot \frac{- 2 y}{3} = - \frac{3}{2} \cdot - 6$

Step 4.1.1.1.4

Cancel the common factor.

$\frac{3 \cdot - 1}{2} \cdot \frac{- 2 y}{3} = - \frac{3}{2} \cdot - 6$

Step 4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{2} (- 2 y) = - \frac{3}{2} \cdot - 6$

Step 4.1.1.2

Cancel the common factor of $2$ .

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Step 4.1.1.2.1

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

$\frac{- 1}{2} (2 (- y)) = - \frac{3}{2} \cdot - 6$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{2} (2 (- y)) = - \frac{3}{2} \cdot - 6$

Step 4.1.1.2.3

Rewrite the expression.

$- - y = - \frac{3}{2} \cdot - 6$

Step 4.1.1.3

Multiply.

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Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 y = - \frac{3}{2} \cdot - 6$

Step 4.1.1.3.2

Multiply $y$ by $1$ .

$y = - \frac{3}{2} \cdot - 6$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- \frac{3}{2} \cdot - 6$ .

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Step 4.2.1.1

Cancel the common factor of $2$ .

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Step 4.2.1.1.1

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$y = \frac{- 3}{2} \cdot - 6$

Step 4.2.1.1.2

Factor $2$ out of $- 6$ .

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

Step 4.2.1.1.3

Cancel the common factor.

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

Step 4.2.1.1.4

Rewrite the expression.

$y = - 3 \cdot - 3$

Step 4.2.1.2

Multiply $- 3$ by $- 3$ .

$y = 9$