Basic Math Examples

$12 - \frac{3}{2} y = 4$

Step 1

Simplify each term.

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Step 1.1

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

$12 - \frac{y \cdot 3}{2} = 4$

Step 1.2

Move $3$ to the left of $y$ .

$12 - \frac{3 y}{2} = 4$

Step 2

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

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Step 2.1

Subtract $12$ from both sides of the equation.

$- \frac{3 y}{2} = 4 - 12$

Step 2.2

Subtract $12$ from $4$ .

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

Step 3

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

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

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

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Step 4.1.1.1

Cancel the common factor of $2$ .

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Step 4.1.1.1.1

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

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

Step 4.1.1.1.2

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

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

Step 4.1.1.1.3

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{3} \cdot \frac{- 3 y}{2} = - \frac{2}{3} \cdot - 8$

Step 4.1.1.1.4

Cancel the common factor.

$\frac{2 \cdot - 1}{3} \cdot \frac{- 3 y}{2} = - \frac{2}{3} \cdot - 8$

Step 4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{3} (- 3 y) = - \frac{2}{3} \cdot - 8$

Step 4.1.1.2

Cancel the common factor of $3$ .

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Step 4.1.1.2.1

Factor $3$ out of $- 3 y$ .

$\frac{- 1}{3} (3 (- y)) = - \frac{2}{3} \cdot - 8$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{3} (3 (- y)) = - \frac{2}{3} \cdot - 8$

Step 4.1.1.2.3

Rewrite the expression.

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

Step 4.1.1.3

Multiply.

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Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 y = - \frac{2}{3} \cdot - 8$

Step 4.1.1.3.2

Multiply $y$ by $1$ .

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

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- \frac{2}{3} \cdot - 8$ .

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Step 4.2.1.1

Multiply $- 8$ by $- 1$ .

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

Step 4.2.1.2

Combine $8$ and $\frac{2}{3}$ .

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

Step 4.2.1.3

Multiply $8$ by $2$ .

$y = \frac{16}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = \frac{16}{3}$

Decimal Form:

$y = 5.\overline{3}$

Mixed Number Form:

$y = 5 \frac{1}{3}$