Solve the Inequality for x x^(4/3)<=27

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

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

$x \approx - 11.84466611, 11.84466611$

Use each root to create test intervals.

$x < - 11.84466611$

$- 11.84466611 < x < 11.84466611$

$x > 11.84466611$

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

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

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

$x = - 14$

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

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

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

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

$x = 0$

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

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

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

True

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

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

$x = 14$

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

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

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

False

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

$x < - 11.84466611$ +(-14)^+4/3^<=+27

$- 11.84466611 < x < 11.84466611$ True

$x > 11.84466611$ False

$x < - 11.84466611$ +(-14)^+4/3^<=+27

$- 11.84466611 < x < 11.84466611$ True

$x > 11.84466611$ False

The solution consists of all of the true intervals.

$- 11.84466611 \leq x \leq 11.84466611$

The result can be shown in multiple forms.

Inequality Form:

$- 11.84466611 \leq x \leq 11.84466611$

Interval Notation:

$[- 11.84466611, 11.84466611]$