Algebra Examples

$x^{\frac{4}{3}} \leq 27$

Step 1

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx - 11.84466611, 11.84466611$

Step 2

Use each root to create test intervals.

$x < - 11.84466611$

$- 11.84466611 < x < 11.84466611$

$x > 11.84466611$

Step 3

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 3.1

Test a value on the interval $x < - 11.84466611$ to see if it makes the inequality true.

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Step 3.1.1

Choose a value on the interval $x < - 11.84466611$ and see if this value makes the original inequality true.

$x = - 14$

Step 3.1.2

Replace $x$ with $- 14$ in the original inequality.

${(- 14)}^{\frac{4}{3}} \leq 27$

Step 3.1.3

The left side $33.74199169$ is greater than the right side $27$ , which means that the given statement is false.

False

Step 3.2

Test a value on the interval $- 11.84466611 < x < 11.84466611$ to see if it makes the inequality true.

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Step 3.2.1

Choose a value on the interval $- 11.84466611 < x < 11.84466611$ and see if this value makes the original inequality true.

$x = 0$

Step 3.2.2

Replace $x$ with $0$ in the original inequality.

${(0)}^{\frac{4}{3}} \leq 27$

Step 3.2.3

The left side $0$ is less than the right side $27$ , which means that the given statement is always true.

True

Step 3.3

Test a value on the interval $x > 11.84466611$ to see if it makes the inequality true.

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Step 3.3.1

Choose a value on the interval $x > 11.84466611$ and see if this value makes the original inequality true.

$x = 14$

Step 3.3.2

Replace $x$ with $14$ in the original inequality.

${(14)}^{\frac{4}{3}} \leq 27$

Step 3.3.3

The left side $33.74199169$ is greater than the right side $27$ , which means that the given statement is false.

False

Step 3.4

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

$x < - 11.84466611$ False

$- 11.84466611 < x < 11.84466611$ True

$x > 11.84466611$ False

$x < - 11.84466611$ False

$- 11.84466611 < x < 11.84466611$ True

$x > 11.84466611$ False

Step 4

The solution consists of all of the true intervals.

$- 11.84466611 \leq x \leq 11.84466611$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$- 11.84466611 \leq x \leq 11.84466611$

Interval Notation:

$[- 11.84466611, 11.84466611]$

Step 6