Trigonometry Examples

$y - 16 = - 3 (x - 12)$

Step 1

Rewrite the equation as $- 3 (x - 12) = y - 16$ .

$- 3 (x - 12) = y - 16$

Step 2

Divide each term in $- 3 (x - 12) = y - 16$ by $- 3$ and simplify.

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Step 2.1

Divide each term in $- 3 (x - 12) = y - 16$ by $- 3$ .

$\frac{- 3 (x - 12)}{- 3} = \frac{y}{- 3} + \frac{- 16}{- 3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 3 (x - 12)}{- 3} = \frac{y}{- 3} + \frac{- 16}{- 3}$

Step 2.2.1.2

Divide $x - 12$ by $1$ .

$x - 12 = \frac{y}{- 3} + \frac{- 16}{- 3}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Move the negative in front of the fraction.

$x - 12 = - \frac{y}{3} + \frac{- 16}{- 3}$

Step 2.3.1.2

Dividing two negative values results in a positive value.

$x - 12 = - \frac{y}{3} + \frac{16}{3}$

Step 3

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

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Step 3.1

Add $12$ to both sides of the equation.

$x = - \frac{y}{3} + \frac{16}{3} + 12$

Step 3.2

To write $12$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x = - \frac{y}{3} + \frac{16}{3} + 12 \cdot \frac{3}{3}$

Step 3.3

Combine $12$ and $\frac{3}{3}$ .

$x = - \frac{y}{3} + \frac{16}{3} + \frac{12 \cdot 3}{3}$

Step 3.4

Combine the numerators over the common denominator.

$x = - \frac{y}{3} + \frac{16 + 12 \cdot 3}{3}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $12$ by $3$ .

$x = - \frac{y}{3} + \frac{16 + 36}{3}$

Step 3.5.2

Add $16$ and $36$ .

$x = - \frac{y}{3} + \frac{52}{3}$