Finite Math Examples

$f (x) y = x^{2 + 5 x - 6}$

Step 1

Solve the equation for $y$ .

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Step 1.1

Subtract $6$ from $2$ .

$f (x) y = x^{5 x - 4}$

Step 1.2

Divide each term in $f (x) y = x^{5 x - 4}$ by $f (x)$ and simplify.

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Step 1.2.1

Divide each term in $f (x) y = x^{5 x - 4}$ by $f (x)$ .

$\frac{f (x) y}{f (x)} = \frac{x^{5 x - 4}}{f (x)}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Reorder factors in $\frac{f (x) y}{f (x)}$ .

$\frac{y f (x)}{f (x)} = \frac{x^{5 x - 4}}{f (x)}$

Step 1.3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$y f x = x^{5 x - 4}$

Step 1.4

Divide each term in $y f x = x^{5 x - 4}$ by $f x$ and simplify.

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Step 1.4.1

Divide each term in $y f x = x^{5 x - 4}$ by $f x$ .

$\frac{y f x}{f x} = \frac{x^{5 x - 4}}{f x}$

Step 1.4.2

Simplify the left side.

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Step 1.4.2.1

Cancel the common factor of $f$ .

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Step 1.4.2.1.1

Cancel the common factor.

$\frac{y f x}{f x} = \frac{x^{5 x - 4}}{f x}$

Step 1.4.2.1.2

Rewrite the expression.

$\frac{y x}{x} = \frac{x^{5 x - 4}}{f x}$

Step 1.4.2.2

Cancel the common factor of $x$ .

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Step 1.4.2.2.1

Cancel the common factor.

$\frac{y x}{x} = \frac{x^{5 x - 4}}{f x}$

Step 1.4.2.2.2

Divide $y$ by $1$ .

$y = \frac{x^{5 x - 4}}{f x}$

Step 1.4.3

Simplify the right side.

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Step 1.4.3.1

Cancel the common factor of $x^{5 x - 4}$ and $x$ .

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Step 1.4.3.1.1

Factor $x$ out of $x^{5 x - 4}$ .

$y = \frac{x \cdot x^{5 x - 5}}{f x}$

Step 1.4.3.1.2

Cancel the common factors.

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Step 1.4.3.1.2.1

Factor $x$ out of $f x$ .

$y = \frac{x \cdot x^{5 x - 5}}{x f}$

Step 1.4.3.1.2.2

Cancel the common factor.

$y = \frac{x \cdot x^{5 x - 5}}{x f}$

Step 1.4.3.1.2.3

Rewrite the expression.

$y = \frac{x^{5 x - 5}}{f}$

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 the variable in the equation violates the linear equation definition, which means that the equation is not a linear equation.

Not Linear