Finite Math Examples

$\frac{f (x)}{g (x)} \cdot x > 1$

Step 1

Simplify the left side.

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Step 1.1

Cancel the common factor of $x$ .

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Step 1.1.1

Factor $x$ out of $g x$ .

$\frac{f (x)}{x g} \cdot x > 1$

Step 1.1.2

Cancel the common factor.

$\frac{f (x)}{x g} \cdot x > 1$

Step 1.1.3

Rewrite the expression.

$\frac{f (x)}{g} > 1$

Step 2

Subtract $1$ from both sides of the inequality.

$\frac{f (x)}{g} - 1 > 0$

Step 3

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

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Step 3.1

Subtract $\frac{f (x)}{g}$ from both sides of the inequality.

$- 1 > - \frac{f (x)}{g}$

Step 3.2

Add $1$ to both sides of the inequality.

$0 > - \frac{f (x)}{g} + 1$

Step 4

The variable $x$ got canceled.

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$