Solve the following inequality. $$ (x-5)(x-2)^{2}(x-7) \geq 0 $$ Write your answer as an interval or union of intervals. If there is no real solution, click on "No solution".

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$$ x \in (-\infty,5] \cup [7,+\infty) $$ Solve the equation $$ (x-5)(x-2)^{2}(x-7) \geq 0 $$. Solve the inequality by following steps: - step0: Solve the inequality by testing the values in the interval: $$\left(x-5ight)\left(x-2ight)^{2}\left(x-7ight)\geq 0$$ - step1: Rewrite the expression: $$\left(x-5ight)\left(x-2ight)^{2}\left(x-7ight)=0$$ - step2: Separate into possible cases: $$\begin{align}&x-5=0\&\left(x-2ight)^{2}=0\&x-7=0\end{align}$$ - step3: Solve the equation: $$\begin{align}&x=5\&x=2\&x=7\end{align}$$ - step4: Determine the test intervals: $$\begin{align}&x<2\&27\end{align}$$ - step5: Choose a value: $$\begin{align}&x_{1}=1\&x_{2}=4\&x_{3}=6\&x_{4}=8\end{align}$$ - step6: Test the chosen value: $$\begin{align}&x<2	extrm{ }	extrm{is the solution}\&27	extrm{ }	extrm{is the solution}\end{align}$$ - step7: Include the critical value: $$\begin{align}&x\leq 2	extrm{ }	extrm{is the solution}\&2\leq x\leq 5	extrm{ }	extrm{is the solution}\&x\geq 7	extrm{ }	extrm{is the solution}\end{align}$$ - step8: The final solution is $$x \in \left(-\infty,5ight]\cup \left[7,+\inftyight):$$ $$x \in \left(-\infty,5ight]\cup \left[7,+\inftyight)$$ The solution to the inequality $$(x-5)(x-2)^{2}(x-7) \geq 0$$ is $$x \in (-\infty,5] \cup [7,+\infty)$$.

Solve the following inequality. \[ (x-5)(x-2)^{2}(x-7) \geq 0 \] Write your answer as an interval or union of intervals. If there is no real solution, click on "No solution".

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Solve the following inequality. \[ (x-5)(x-2)^{2}(x-7) \geq 0 \] Write your answer as an interval or union of intervals. If there is no real solution, click on "No solution".

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