Trigonometry Examples

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

Step 1

Rewrite the equation as $\frac{3}{4} \cdot (x - 3) = y + 4$ .

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

Step 2

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

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

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

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

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Step 3.1.1.1

Apply the distributive property.

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

Step 3.1.1.2

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

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

Step 3.1.1.3

Multiply $\frac{3}{4} \cdot - 3$ .

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Step 3.1.1.3.1

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

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

Step 3.1.1.3.2

Multiply $3$ by $- 3$ .

$\frac{4}{3} (\frac{3 x}{4} + \frac{- 9}{4}) = \frac{4}{3} (y + 4)$

Step 3.1.1.4

Move the negative in front of the fraction.

$\frac{4}{3} (\frac{3 x}{4} - \frac{9}{4}) = \frac{4}{3} (y + 4)$

Step 3.1.1.5

Apply the distributive property.

$\frac{4}{3} \cdot \frac{3 x}{4} + \frac{4}{3} (- \frac{9}{4}) = \frac{4}{3} (y + 4)$

Step 3.1.1.6

Cancel the common factor of $4$ .

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Step 3.1.1.6.1

Cancel the common factor.

$\frac{4}{3} \cdot \frac{3 x}{4} + \frac{4}{3} (- \frac{9}{4}) = \frac{4}{3} (y + 4)$

Step 3.1.1.6.2

Rewrite the expression.

$\frac{1}{3} (3 x) + \frac{4}{3} (- \frac{9}{4}) = \frac{4}{3} (y + 4)$

Step 3.1.1.7

Cancel the common factor of $3$ .

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Step 3.1.1.7.1

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) + \frac{4}{3} (- \frac{9}{4}) = \frac{4}{3} (y + 4)$

Step 3.1.1.7.2

Cancel the common factor.

$\frac{1}{3} (3 x) + \frac{4}{3} (- \frac{9}{4}) = \frac{4}{3} (y + 4)$

Step 3.1.1.7.3

Rewrite the expression.

$x + \frac{4}{3} (- \frac{9}{4}) = \frac{4}{3} (y + 4)$

Step 3.1.1.8

Cancel the common factor of $4$ .

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Step 3.1.1.8.1

Move the leading negative in $- \frac{9}{4}$ into the numerator.

$x + \frac{4}{3} \cdot \frac{- 9}{4} = \frac{4}{3} (y + 4)$

Step 3.1.1.8.2

Cancel the common factor.

$x + \frac{4}{3} \cdot \frac{- 9}{4} = \frac{4}{3} (y + 4)$

Step 3.1.1.8.3

Rewrite the expression.

$x + \frac{1}{3} \cdot - 9 = \frac{4}{3} (y + 4)$

Step 3.1.1.9

Cancel the common factor of $3$ .

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Step 3.1.1.9.1

Factor $3$ out of $- 9$ .

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

Step 3.1.1.9.2

Cancel the common factor.

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

Step 3.1.1.9.3

Rewrite the expression.

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

Step 3.2

Simplify the right side.

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Step 3.2.1

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

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Step 3.2.1.1

Apply the distributive property.

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

Step 3.2.1.2

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

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

Step 3.2.1.3

Multiply $\frac{4}{3} \cdot 4$ .

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Step 3.2.1.3.1

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

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

Step 3.2.1.3.2

Multiply $4$ by $4$ .

$x - 3 = \frac{4 y}{3} + \frac{16}{3}$

Step 4

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

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Step 4.1

Add $3$ to both sides of the equation.

$x = \frac{4 y}{3} + \frac{16}{3} + 3$

Step 4.2

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

$x = \frac{4 y}{3} + \frac{16}{3} + 3 \cdot \frac{3}{3}$

Step 4.3

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

$x = \frac{4 y}{3} + \frac{16}{3} + \frac{3 \cdot 3}{3}$

Step 4.4

Combine the numerators over the common denominator.

$x = \frac{4 y}{3} + \frac{16 + 3 \cdot 3}{3}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $3$ by $3$ .

$x = \frac{4 y}{3} + \frac{16 + 9}{3}$

Step 4.5.2

Add $16$ and $9$ .

$x = \frac{4 y}{3} + \frac{25}{3}$