If 3x−3<3+
2
x
​
and x−2≤6+2x, then x can take which of the following values?

Let us solve the two inequalities separately.
First Inequality:

3x−3<3+
2
x
​

Multiply the entire inequality by 2 to clear the fraction:

6x−6<6+x
6x−x<6+6
5x<12
x<
5
12
​
=2.4
Second Inequality:

x−2≤6+2x
x−2x≤6+2
−x≤8
Multiplying by −1 flips the inequality sign:

x≥−8
Combining both results, the range for x is:

−8≤x<2.4
Among the given options:

A) 6 (Not in range)

B) 2 (In range)

C) 10 (Not in range)

D) −10 (Not in range)

Thus, x can take the value 2.