Trigonometry Examples

$- \frac{3}{4} x - 3 y = \frac{- 15}{2}$

Step 1

Simplify each term.

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Step 1.1

Combine $x$ and $\frac{3}{4}$ .

$- \frac{x \cdot 3}{4} - 3 y = \frac{- 15}{2}$

Step 1.2

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

$- \frac{3 x}{4} - 3 y = \frac{- 15}{2}$

Step 2

Move the negative in front of the fraction.

$- \frac{3 x}{4} - 3 y = - \frac{15}{2}$

Step 3

Add $3 y$ to both sides of the equation.

$- \frac{3 x}{4} = - \frac{15}{2} + 3 y$

Step 4

Multiply both sides of the equation by $- \frac{4}{3}$ .

$- \frac{4}{3} (- \frac{3 x}{4}) = - \frac{4}{3} (- \frac{15}{2} + 3 y)$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $- \frac{4}{3} (- \frac{3 x}{4})$ .

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Step 5.1.1.1

Cancel the common factor of $4$ .

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Step 5.1.1.1.1

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$\frac{- 4}{3} (- \frac{3 x}{4}) = - \frac{4}{3} (- \frac{15}{2} + 3 y)$

Step 5.1.1.1.2

Move the leading negative in $- \frac{3 x}{4}$ into the numerator.

$\frac{- 4}{3} \cdot \frac{- 3 x}{4} = - \frac{4}{3} (- \frac{15}{2} + 3 y)$

Step 5.1.1.1.3

Factor $4$ out of $- 4$ .

$\frac{4 (- 1)}{3} \cdot \frac{- 3 x}{4} = - \frac{4}{3} (- \frac{15}{2} + 3 y)$

Step 5.1.1.1.4

Cancel the common factor.

$\frac{4 \cdot - 1}{3} \cdot \frac{- 3 x}{4} = - \frac{4}{3} (- \frac{15}{2} + 3 y)$

Step 5.1.1.1.5

Rewrite the expression.

$\frac{- 1}{3} (- 3 x) = - \frac{4}{3} (- \frac{15}{2} + 3 y)$

Step 5.1.1.2

Cancel the common factor of $3$ .

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Step 5.1.1.2.1

Factor $3$ out of $- 3 x$ .

$\frac{- 1}{3} (3 (- x)) = - \frac{4}{3} (- \frac{15}{2} + 3 y)$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{- 1}{3} (3 (- x)) = - \frac{4}{3} (- \frac{15}{2} + 3 y)$

Step 5.1.1.2.3

Rewrite the expression.

$- - x = - \frac{4}{3} (- \frac{15}{2} + 3 y)$

Step 5.1.1.3

Multiply.

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Step 5.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{4}{3} (- \frac{15}{2} + 3 y)$

Step 5.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{4}{3} (- \frac{15}{2} + 3 y)$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $- \frac{4}{3} (- \frac{15}{2} + 3 y)$ .

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Step 5.2.1.1

Apply the distributive property.

$x = - \frac{4}{3} (- \frac{15}{2}) - \frac{4}{3} (3 y)$

Step 5.2.1.2

Cancel the common factor of $2$ .

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Step 5.2.1.2.1

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$x = \frac{- 4}{3} (- \frac{15}{2}) - \frac{4}{3} (3 y)$

Step 5.2.1.2.2

Move the leading negative in $- \frac{15}{2}$ into the numerator.

$x = \frac{- 4}{3} \cdot \frac{- 15}{2} - \frac{4}{3} (3 y)$

Step 5.2.1.2.3

Factor $2$ out of $- 4$ .

$x = \frac{2 (- 2)}{3} \cdot \frac{- 15}{2} - \frac{4}{3} (3 y)$

Step 5.2.1.2.4

Cancel the common factor.

$x = \frac{2 \cdot - 2}{3} \cdot \frac{- 15}{2} - \frac{4}{3} (3 y)$

Step 5.2.1.2.5

Rewrite the expression.

$x = \frac{- 2}{3} \cdot - 15 - \frac{4}{3} (3 y)$

Step 5.2.1.3

Cancel the common factor of $3$ .

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Step 5.2.1.3.1

Factor $3$ out of $- 15$ .

$x = \frac{- 2}{3} \cdot (3 (- 5)) - \frac{4}{3} (3 y)$

Step 5.2.1.3.2

Cancel the common factor.

$x = \frac{- 2}{3} \cdot (3 \cdot - 5) - \frac{4}{3} (3 y)$

Step 5.2.1.3.3

Rewrite the expression.

$x = - 2 \cdot - 5 - \frac{4}{3} (3 y)$

Step 5.2.1.4

Multiply $- 2$ by $- 5$ .

$x = 10 - \frac{4}{3} (3 y)$

Step 5.2.1.5

Cancel the common factor of $3$ .

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Step 5.2.1.5.1

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$x = 10 + \frac{- 4}{3} (3 y)$

Step 5.2.1.5.2

Factor $3$ out of $3 y$ .

$x = 10 + \frac{- 4}{3} (3 (y))$

Step 5.2.1.5.3

Cancel the common factor.

$x = 10 + \frac{- 4}{3} (3 y)$

Step 5.2.1.5.4

Rewrite the expression.

$x = 10 - 4 y$

Step 6

Reorder $10$ and $- 4 y$ .

$x = - 4 y + 10$