Solve the inequality. Write the solution set in interval notation if possible. $$ \frac{(2-x)(2 x+1)^{2}}{(x-4)^{4}} \leq 0 $$ The solution set is $$ \square . \square(\square, \square)[\square, \square] \quad(\square, \square] $$

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Solve the equation $$ \frac{(2-x)(2 x+1)^{2}}{(x-4)^{4}} \leq 0 $$.
Solve the inequality by following steps:
- step0: Solve the inequality by testing the values in the interval:
  $$\frac{\left(2-xight)\left(2x+1ight)^{2}}{\left(x-4ight)^{4}}\leq 0$$
- step1: Find the domain:
  $$\frac{\left(2-xight)\left(2x+1ight)^{2}}{\left(x-4ight)^{4}}\leq 0,x
eq 4$$
- step2: Set the numerator and denominator of $$\frac{\left(2-xight)\left(2x+1ight)^{2}}{\left(x-4ight)^{4}}$$ equal to 0$$:$$
  $$\begin{align}&\left(2-xight)\left(2x+1ight)^{2}=0\&\left(x-4ight)^{4}=0\end{align}$$
- step3: Calculate:
  $$\begin{align}&x=2\&x=-\frac{1}{2}\&x=4\end{align}$$
- step4: Determine the test intervals:
  $$\begin{align}&x<-\frac{1}{2}\&-\frac{1}{2}4\end{align}$$
- step5: Choose a value:
  $$\begin{align}&x_{1}=-2\&x_{2}=1\&x_{3}=3\&x_{4}=5\end{align}$$
- step6: Test the chosen value:
  $$\begin{align}&x<-\frac{1}{2}	extrm{ }	extrm{is not a solution}\&-\frac{1}{2}4	extrm{ }	extrm{is the solution}\end{align}$$
- step7: Include the critical value:
  $$\begin{align}&2\leq x<4	extrm{ }	extrm{is the solution}\&x>4	extrm{ }	extrm{is the solution}\&x=-\frac{1}{2}\end{align}$$
- step8: The final solution is $$x \in \left[2,4ight)\cup \left(4,+\inftyight)\cup \left\{-\frac{1}{2}ight\}:$$
  $$x \in \left[2,4ight)\cup \left(4,+\inftyight)\cup \left\{-\frac{1}{2}ight\}$$
- step9: Check if the solution is in the defined range:
  $$x \in \left[2,4ight)\cup \left(4,+\inftyight)\cup \left\{-\frac{1}{2}ight\},x
eq 4$$
- step10: Find the intersection:
  $$x \in \left[2,4ight)\cup \left(4,+\inftyight)\cup \left\{-\frac{1}{2}ight\}$$
The solution set for the inequality $$ \frac{(2-x)(2 x+1)^{2}}{(x-4)^{4}} \leq 0 $$ is $$ x \in [2,4) \cup (4,+\infty) \cup \{-0.5\} $$ or $$ x \in [2,4) \cup (4,+\infty) \cup \{-\frac{1}{2}\} $$.
The solution set is $$ x \in [2, 4) \cup (4, +\infty) \cup \{-0.5\} $$.

Solve the inequality. Write the solution set in interval notation if possible.

The solution set is

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