If 5x−3≥3+
2
x
​
and 4x−2≤6+x, then x can take which of the following values?

Solve the first inequality:
5x−3≥3+
2
x
​

Multiply the entire inequality by 2 to clear the fraction:

10x−6≥6+x
10x−x≥6+6
9x≥12
x≥
9
12
​
⟹x≥
3
4
​
⟹x≥1.33
Solve the second inequality:

4x−2≤6+x
4x−x≤6+2
3x≤8
x≤
3
8
​
⟹x≤2.67
Combining both inequalities, we get the range for x:

3
4
​
≤x≤
3
8
​
⟹1.33≤x≤2.67
Among the given options, only 2 falls within this interval.