Solve the inequality: $$ \frac{x-2}{x-8} \geq 0 $$ Interval notation solution: No solution

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The correct interval notation solution is $$ x \in (-\infty,2] \cup (8,+\infty) $$. Solve the equation $$ \frac{x-2}{x-8} \geq 0 $$. Solve the inequality by following steps: - step0: Solve the inequality by testing the values in the interval: $$\frac{x-2}{x-8}\geq 0$$ - step1: Find the domain: $$\frac{x-2}{x-8}\geq 0,x
eq 8$$ - step2: Set the numerator and denominator of $$\frac{x-2}{x-8}$$ equal to 0$$:$$ $$\begin{align}&x-2=0\&x-8=0\end{align}$$ - step3: Calculate: $$\begin{align}&x=2\&x=8\end{align}$$ - step4: Determine the test intervals: $$\begin{align}&x<2\&28\end{align}$$ - step5: Choose a value: $$\begin{align}&x_{1}=1\&x_{2}=5\&x_{3}=9\end{align}$$ - step6: Test the chosen value: $$\begin{align}&x<2	extrm{ }	extrm{is the solution}\&28	extrm{ }	extrm{is the solution}\end{align}$$ - step7: Include the critical value: $$\begin{align}&x\leq 2	extrm{ }	extrm{is the solution}\&x>8	extrm{ }	extrm{is the solution}\end{align}$$ - step8: The final solution is $$x \in \left(-\infty,2ight]\cup \left(8,+\inftyight):$$ $$x \in \left(-\infty,2ight]\cup \left(8,+\inftyight)$$ - step9: Check if the solution is in the defined range: $$x \in \left(-\infty,2ight]\cup \left(8,+\inftyight),x
eq 8$$ - step10: Find the intersection: $$x \in \left(-\infty,2ight]\cup \left(8,+\inftyight)$$ The solution to the inequality $$ \frac{x-2}{x-8} \geq 0 $$ is $$ x \in (-\infty,2] \cup (8,+\infty) $$. However, the interval notation solution provided is "No solution", which is incorrect. The correct interval notation solution is $$ x \in (-\infty,2] \cup (8,+\infty) $$.

Solve the inequality: \( \frac{x-2}{x-8} \geq 0 \) Interval notation solution: No solution

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Solve the inequality: \( \frac{x-2}{x-8} \geq 0 \) Interval notation solution: No solution

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