Trigonometry Examples

$f (x) = \frac{3 x + 5}{3 x - B}$ , $f (x) = 2$

Step 1

Substitute $2$ for $f (x)$ .

$2 = \frac{3 x + 5}{3 x - B}$

Step 2

Solve for $x$ .

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Step 2.1

Rewrite the equation as $\frac{3 x + 5}{3 x - B} = 2$ .

$\frac{3 x + 5}{3 x - B} = 2$

Step 2.2

Find the LCD of the terms in the equation.

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Step 2.2.1

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

$3 x - B, 1$

Step 2.2.2

Remove parentheses.

$3 x - B, 1$

Step 2.2.3

The LCM of one and any expression is the expression.

$3 x - B$

Step 2.3

Multiply each term in $\frac{3 x + 5}{3 x - B} = 2$ by $3 x - B$ to eliminate the fractions.

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Step 2.3.1

Multiply each term in $\frac{3 x + 5}{3 x - B} = 2$ by $3 x - B$ .

$\frac{3 x + 5}{3 x - B} (3 x - B) = 2 (3 x - B)$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $3 x - B$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{3 x + 5}{3 x - B} (3 x - B) = 2 (3 x - B)$

Step 2.3.2.1.2

Rewrite the expression.

$3 x + 5 = 2 (3 x - B)$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Apply the distributive property.

$3 x + 5 = 2 (3 x) + 2 (- B)$

Step 2.3.3.2

Multiply.

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Step 2.3.3.2.1

Multiply $3$ by $2$ .

$3 x + 5 = 6 x + 2 (- B)$

Step 2.3.3.2.2

Multiply $- 1$ by $2$ .

$3 x + 5 = 6 x - 2 B$

Step 2.4

Solve the equation.

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Step 2.4.1

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

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Step 2.4.1.1

Subtract $6 x$ from both sides of the equation.

$3 x + 5 - 6 x = - 2 B$

Step 2.4.1.2

Subtract $6 x$ from $3 x$ .

$- 3 x + 5 = - 2 B$

Step 2.4.2

Subtract $5$ from both sides of the equation.

$- 3 x = - 2 B - 5$

Step 2.4.3

Divide each term in $- 3 x = - 2 B - 5$ by $- 3$ and simplify.

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Step 2.4.3.1

Divide each term in $- 3 x = - 2 B - 5$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 2 B}{- 3} + \frac{- 5}{- 3}$

Step 2.4.3.2

Simplify the left side.

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Step 2.4.3.2.1

Cancel the common factor of $- 3$ .

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Step 2.4.3.2.1.1

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 2 B}{- 3} + \frac{- 5}{- 3}$

Step 2.4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 2 B}{- 3} + \frac{- 5}{- 3}$

Step 2.4.3.3

Simplify the right side.

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Step 2.4.3.3.1

Simplify each term.

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Step 2.4.3.3.1.1

Dividing two negative values results in a positive value.

$x = \frac{2 B}{3} + \frac{- 5}{- 3}$

Step 2.4.3.3.1.2

Dividing two negative values results in a positive value.

$x = \frac{2 B}{3} + \frac{5}{3}$