Trigonometry Examples

$(13 x + 5) (8 y + 7) = 180$

Step 1

Solve the equation for $y$ .

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Step 1.1

Divide each term in $(13 x + 5) (8 y + 7) = 180$ by $13 x + 5$ and simplify.

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Step 1.1.1

Divide each term in $(13 x + 5) (8 y + 7) = 180$ by $13 x + 5$ .

$\frac{(13 x + 5) (8 y + 7)}{13 x + 5} = \frac{180}{13 x + 5}$

Step 1.1.2

Simplify the left side.

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Step 1.1.2.1

Cancel the common factor of $13 x + 5$ .

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Step 1.1.2.1.1

Cancel the common factor.

$\frac{(13 x + 5) (8 y + 7)}{13 x + 5} = \frac{180}{13 x + 5}$

Step 1.1.2.1.2

Divide $8 y + 7$ by $1$ .

$8 y + 7 = \frac{180}{13 x + 5}$

Step 1.2

Subtract $7$ from both sides of the equation.

$8 y = \frac{180}{13 x + 5} - 7$

Step 1.3

Divide each term in $8 y = \frac{180}{13 x + 5} - 7$ by $8$ and simplify.

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Step 1.3.1

Divide each term in $8 y = \frac{180}{13 x + 5} - 7$ by $8$ .

$\frac{8 y}{8} = \frac{\frac{180}{13 x + 5}}{8} + \frac{- 7}{8}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $8$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{8 y}{8} = \frac{\frac{180}{13 x + 5}}{8} + \frac{- 7}{8}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{\frac{180}{13 x + 5}}{8} + \frac{- 7}{8}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Combine the numerators over the common denominator.

$y = \frac{\frac{180}{13 x + 5} - 7}{8}$

Step 1.3.3.2

To write $- 7$ as a fraction with a common denominator, multiply by $\frac{13 x + 5}{13 x + 5}$ .

$y = \frac{\frac{180}{13 x + 5} - 7 \cdot \frac{13 x + 5}{13 x + 5}}{8}$

Step 1.3.3.3

Simplify terms.

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Step 1.3.3.3.1

Combine $- 7$ and $\frac{13 x + 5}{13 x + 5}$ .

$y = \frac{\frac{180}{13 x + 5} + \frac{- 7 (13 x + 5)}{13 x + 5}}{8}$

Step 1.3.3.3.2

Combine the numerators over the common denominator.

$y = \frac{\frac{180 - 7 (13 x + 5)}{13 x + 5}}{8}$

Step 1.3.3.4

Simplify the numerator.

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Step 1.3.3.4.1

Apply the distributive property.

$y = \frac{\frac{180 - 7 (13 x) - 7 \cdot 5}{13 x + 5}}{8}$

Step 1.3.3.4.2

Multiply $13$ by $- 7$ .

$y = \frac{\frac{180 - 91 x - 7 \cdot 5}{13 x + 5}}{8}$

Step 1.3.3.4.3

Multiply $- 7$ by $5$ .

$y = \frac{\frac{180 - 91 x - 35}{13 x + 5}}{8}$

Step 1.3.3.4.4

Subtract $35$ from $180$ .

$y = \frac{\frac{- 91 x + 145}{13 x + 5}}{8}$

Step 1.3.3.5

Simplify with factoring out.

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Step 1.3.3.5.1

Factor $- 1$ out of $- 91 x$ .

$y = \frac{\frac{- (91 x) + 145}{13 x + 5}}{8}$

Step 1.3.3.5.2

Rewrite $145$ as $- 1 (- 145)$ .

$y = \frac{\frac{- (91 x) - 1 (- 145)}{13 x + 5}}{8}$

Step 1.3.3.5.3

Factor $- 1$ out of $- (91 x) - 1 (- 145)$ .

$y = \frac{\frac{- (91 x - 145)}{13 x + 5}}{8}$

Step 1.3.3.5.4

Simplify the expression.

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Step 1.3.3.5.4.1

Rewrite $- (91 x - 145)$ as $- 1 (91 x - 145)$ .

$y = \frac{\frac{- 1 (91 x - 145)}{13 x + 5}}{8}$

Step 1.3.3.5.4.2

Move the negative in front of the fraction.

$y = \frac{- \frac{91 x - 145}{13 x + 5}}{8}$

Step 1.3.3.6

Multiply the numerator by the reciprocal of the denominator.

$y = - \frac{91 x - 145}{13 x + 5} \cdot \frac{1}{8}$

Step 1.3.3.7

Multiply $\frac{1}{8}$ by $\frac{91 x - 145}{13 x + 5}$ .

$y = - \frac{91 x - 145}{8 (13 x + 5)}$

Step 2

A linear equation is an equation of a straight line, which means that the degree of a linear equation must be $0$ or $1$ for each of its variables. In this case, the degree of variable $y$ is $1$ , the degrees of the variables in the equation violate the linear equation definition, which means that the equation is not a linear equation.

Not Linear