2 times the answer of x is greater than or equal to 6 and less than x. Find the range of x.

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.

Explore the solution to the compound inequalities 2x ≥ 6 and 2x < x. This problem involves understanding and solving linear inequalities, and is suitable for students in Grades 8-10. Learn how to combine inequalities and determine if a solution exists.

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