We need to solve the inequality given by the problem:

$2x \geq 6 \text{ and } 2x < x$

Step 1: Solve the first inequality $2x \geq 6$

To solve $2x \geq 6$:

$x \geq \frac{6}{2} = 3$

Step 2: Solve the second inequality $2x < x$

To solve $2x < x$:

$2x - x < 0 \implies x < 0$

Step 3: Combine the inequalities

Now, let's combine the two conditions:

1. $x \geq 3$
2. $x < 0$

These two conditions cannot be true at the same time because there is no $x$ that satisfies $x \geq 3$ and $x < 0$ simultaneously.

Conclusion

There is no value of $x$ that satisfies both inequalities. Therefore, there is no range of $x$ that meets the given conditions.

Would you like further details on this problem, or do you have any questions?

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Here are 5 related questions for further exploration:

1. What if the inequality was $2x > 6$ and $2x \leq x$?
2. How would the solution change if the inequalities were combined into a single inequality?
3. Can you provide an example where $2x < 6$ and $x > 0$?
4. How would the range of $x$ change if the inequalities were $2x \leq 6$ and $2x > x$?
5. How do you solve a system of linear inequalities?

Tip: Always check if a solution satisfies all parts of a compound inequality when combining them.