Trigonometry Examples

$\frac{x + 16}{x - 2} = 7$

Step 1

Find the LCD of the terms in the equation.

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Step 1.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x - 2, 1$

Step 1.2

Remove parentheses.

$x - 2, 1$

Step 1.3

The LCM of one and any expression is the expression.

$x - 2$

Step 2

Multiply each term in $\frac{x + 16}{x - 2} = 7$ by $x - 2$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{x + 16}{x - 2} = 7$ by $x - 2$ .

$\frac{x + 16}{x - 2} (x - 2) = 7 (x - 2)$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $x - 2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{x + 16}{x - 2} (x - 2) = 7 (x - 2)$

Step 2.2.1.2

Rewrite the expression.

$x + 16 = 7 (x - 2)$

Step 2.3

Simplify the right side.

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Step 2.3.1

Apply the distributive property.

$x + 16 = 7 x + 7 \cdot - 2$

Step 2.3.2

Multiply $7$ by $- 2$ .

$x + 16 = 7 x - 14$

Step 3

Solve the equation.

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Step 3.1

Move all terms containing $x$ to the left side of the equation.

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Step 3.1.1

Subtract $7 x$ from both sides of the equation.

$x + 16 - 7 x = - 14$

Step 3.1.2

Subtract $7 x$ from $x$ .

$- 6 x + 16 = - 14$

Step 3.2

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

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Step 3.2.1

Subtract $16$ from both sides of the equation.

$- 6 x = - 14 - 16$

Step 3.2.2

Subtract $16$ from $- 14$ .

$- 6 x = - 30$

Step 3.3

Divide each term in $- 6 x = - 30$ by $- 6$ and simplify.

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Step 3.3.1

Divide each term in $- 6 x = - 30$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{- 30}{- 6}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 6$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{- 30}{- 6}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 30}{- 6}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $- 30$ by $- 6$ .

$x = 5$