Trigonometry Examples

$f (3 x - 2) = \frac{3 x - 1}{x - 7}$

Step 1

Solve the equation for $f$ .

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Step 1.1

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

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Step 1.1.1

Subtract $f (3 x - 2)$ from both sides of the equation.

$0 = \frac{3 x - 1}{x - 7} - f (3 x - 2)$

Step 1.1.2

Simplify each term.

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Step 1.1.2.1

Split the fraction $\frac{3 x - 1}{x - 7}$ into two fractions.

$0 = \frac{3 x}{x - 7} + \frac{- 1}{x - 7} - f (3 x - 2)$

Step 1.1.2.2

Move the negative in front of the fraction.

$0 = \frac{3 x}{x - 7} - \frac{1}{x - 7} - f (3 x - 2)$

Step 1.2

Rewrite the equation as $\frac{3 x}{x - 7} - \frac{1}{x - 7} - f (3 x - 2) = 0$ .

$\frac{3 x}{x - 7} - \frac{1}{x - 7} - f (3 x - 2) = 0$

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 and the degree of variable $f$ 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