Finite Math Examples

$- \frac{3}{x^{4}} > 0$

Step 1

Find all the values where the expression switches from negative to positive by setting each factor equal to $0$ and solving.

$x^{4} = 0$

Step 2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt[4]{0}$

Step 3

Simplify $\pm \sqrt[4]{0}$ .

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Step 3.1

Rewrite $0$ as $0^{4}$ .

$x = \pm \sqrt[4]{0^{4}}$

Step 3.2

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 0$

Step 3.3

Plus or minus $0$ is $0$ .

$x = 0$

Step 4

Find the domain of $- \frac{3}{x^{4}}$ .

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Step 4.1

Set the denominator in $\frac{3}{x^{4}}$ equal to $0$ to find where the expression is undefined.

$x^{4} = 0$

Step 4.2

Solve for $x$ .

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Step 4.2.1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt[4]{0}$

Step 4.2.2

Simplify $\pm \sqrt[4]{0}$ .

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Step 4.2.2.1

Rewrite $0$ as $0^{4}$ .

$x = \pm \sqrt[4]{0^{4}}$

Step 4.2.2.2

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 0$

Step 4.2.2.3

Plus or minus $0$ is $0$ .

$x = 0$

Step 4.3

The domain is all values of $x$ that make the expression defined.

$(- \infty, 0) \cup (0, \infty)$

Step 5

Use each root to create test intervals.

$x < 0$

$x > 0$

Step 6

Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.

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Step 6.1

Test a value on the interval $x < 0$ to see if it makes the inequality true.

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Step 6.1.1

Choose a value on the interval $x < 0$ and see if this value makes the original inequality true.

$x = - 2$

Step 6.1.2

Replace $x$ with $- 2$ in the original inequality.

$- \frac{3}{{(- 2)}^{4}} > 0$

Step 6.1.3

The left side $- 0.1875$ is not greater than the right side $0$ , which means that the given statement is false.

False

Step 6.2

Test a value on the interval $x > 0$ to see if it makes the inequality true.

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Step 6.2.1

Choose a value on the interval $x > 0$ and see if this value makes the original inequality true.

$x = 2$

Step 6.2.2

Replace $x$ with $2$ in the original inequality.

$- \frac{3}{{(2)}^{4}} > 0$

Step 6.2.3

The left side $- 0.1875$ is not greater than the right side $0$ , which means that the given statement is false.

False

Step 6.3

Compare the intervals to determine which ones satisfy the original inequality.

$x < 0$ False

$x > 0$ False

$x < 0$ False

$x > 0$ False

Step 7

Since there are no numbers that fall within the interval, this inequality has no solution.

No solution