Finite Math Examples

$\frac{1}{x} < \frac{1}{y}$

Step 1

Multiply both sides by $x$ .

$\frac{1}{x} x = \frac{1}{y} x$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $x$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{1}{x} x = \frac{1}{y} x$

Step 2.1.1.2

Rewrite the expression.

$1 = \frac{1}{y} x$

$1 = \frac{1}{y} x$

$1 = \frac{1}{y} x$

Step 2.2

Simplify the right side.

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Step 2.2.1

Combine $\frac{1}{y}$ and $x$ .

$1 = \frac{x}{y}$

$1 = \frac{x}{y}$

$1 = \frac{x}{y}$

Step 3

Solve for $x$ .

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Step 3.1

Rewrite the equation as $\frac{x}{y} = 1$ .

$\frac{x}{y} = 1$

Step 3.2

Multiply both sides by $y$ .

$\frac{x}{y} y = 1 y$

Step 3.3

Simplify.

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Step 3.3.1

Simplify the left side.

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Step 3.3.1.1

Cancel the common factor of $y$ .

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Step 3.3.1.1.1

Cancel the common factor.

$\frac{x}{y} y = 1 y$

Step 3.3.1.1.2

Rewrite the expression.

$x = 1 y$

$x = 1 y$

$x = 1 y$

Step 3.3.2

Simplify the right side.

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Step 3.3.2.1

Multiply $y$ by $1$ .

$x = y$

$x = y$

$x = y$

$x = y$

Step 4

Convert the inequality to interval notation.

$[y, y]$

Step 5

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$