Trigonometry Examples

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

Step 1

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

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

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

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

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Step 2.1.1.1

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

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

Step 2.1.1.2

Cancel the common factor of $3$ .

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Step 2.1.1.2.1

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

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

Step 2.1.1.2.2

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

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

Step 2.1.1.2.3

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{2} \cdot \frac{- y \cdot 2}{3} = - \frac{3}{2} \cdot 12$

Step 2.1.1.2.4

Cancel the common factor.

$\frac{3 \cdot - 1}{2} \cdot \frac{- y \cdot 2}{3} = - \frac{3}{2} \cdot 12$

Step 2.1.1.2.5

Rewrite the expression.

$\frac{- 1}{2} (- y \cdot 2) = - \frac{3}{2} \cdot 12$

Step 2.1.1.3

Cancel the common factor of $2$ .

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Step 2.1.1.3.1

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

$\frac{- 1}{2} (2 \cdot (- y)) = - \frac{3}{2} \cdot 12$

Step 2.1.1.3.2

Cancel the common factor.

$\frac{- 1}{2} (2 \cdot (- y)) = - \frac{3}{2} \cdot 12$

Step 2.1.1.3.3

Rewrite the expression.

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

Step 2.1.1.4

Multiply.

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Step 2.1.1.4.1

Multiply $- 1$ by $- 1$ .

$1 y = - \frac{3}{2} \cdot 12$

Step 2.1.1.4.2

Multiply $y$ by $1$ .

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

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $- \frac{3}{2} \cdot 12$ .

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Step 2.2.1.1

Cancel the common factor of $2$ .

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Step 2.2.1.1.1

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

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

Step 2.2.1.1.2

Factor $2$ out of $12$ .

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

Step 2.2.1.1.3

Cancel the common factor.

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

Step 2.2.1.1.4

Rewrite the expression.

$y = - 3 \cdot 6$

Step 2.2.1.2

Multiply $- 3$ by $6$ .

$y = - 18$