Solve the following inequality. \[ -5 x^{\frac{2}{5}} \leq 6 \] There is no solution. $-1.578 \leq x \leq 1.578$ All real numbers. $x \leq-1.578$ or $x \geq 1.578$

Step 1 ：The inequality is in the form of \(-5x^{2/5} \leq 6\). To solve this inequality, we need to isolate \(x\).

Step 2 ：First, we can divide both sides by -5, which gives \(x^{2/5} \geq -6/5\). Remember that when we divide or multiply an inequality by a negative number, the direction of the inequality sign changes.

Step 3 ：Next, we can raise both sides to the power of 5/2 to get rid of the fractional exponent on the left side. This gives \(x \geq (-6/5)^{5/2}\).

Step 4 ：Finally, we can calculate the value of \((-6/5)^{5/2}\) to find the solution to the inequality.

Step 5 ：The result is a complex number, which is not a real number. This is because we are taking the square root of a negative number, which is not defined in the real number system.

Step 6 ：Therefore, there is no real solution to the inequality.

Step 7 ：\(\boxed{\text{Final Answer: There is no solution.}}\)