Trigonometry Examples

$8 y + 2 x y = 3 x - 1$

Step 1

Subtract $3 x$ from both sides of the equation.

$8 y + 2 x y - 3 x = - 1$

Step 2

Subtract $8 y$ from both sides of the equation.

$2 x y - 3 x = - 1 - 8 y$

Step 3

Factor $x$ out of $2 x y - 3 x$ .

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Step 3.1

Factor $x$ out of $2 x y$ .

$x (2 y) - 3 x = - 1 - 8 y$

Step 3.2

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

$x (2 y) + x \cdot - 3 = - 1 - 8 y$

Step 3.3

Factor $x$ out of $x (2 y) + x \cdot - 3$ .

$x (2 y - 3) = - 1 - 8 y$

Step 4

Divide each term in $x (2 y - 3) = - 1 - 8 y$ by $2 y - 3$ and simplify.

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Step 4.1

Divide each term in $x (2 y - 3) = - 1 - 8 y$ by $2 y - 3$ .

$\frac{x (2 y - 3)}{2 y - 3} = \frac{- 1}{2 y - 3} + \frac{- 8 y}{2 y - 3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2 y - 3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{x (2 y - 3)}{2 y - 3} = \frac{- 1}{2 y - 3} + \frac{- 8 y}{2 y - 3}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 1}{2 y - 3} + \frac{- 8 y}{2 y - 3}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Combine the numerators over the common denominator.

$x = \frac{- 1 - 8 y}{2 y - 3}$

Step 4.3.2

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

$x = \frac{- 1 (1) - 8 y}{2 y - 3}$

Step 4.3.3

Factor $- 1$ out of $- 8 y$ .

$x = \frac{- 1 (1) - (8 y)}{2 y - 3}$

Step 4.3.4

Factor $- 1$ out of $- 1 (1) - (8 y)$ .

$x = \frac{- 1 (1 + 8 y)}{2 y - 3}$

Step 4.3.5

Move the negative in front of the fraction.

$x = - \frac{1 + 8 y}{2 y - 3}$