identify an integer x for which 2x/5 represents a ratio greater that 2:1 but less than 3:1

could 2.4 be a possible answer?

2x/5 > 2/1

2x > 10
x > 10

and

2x/5 < 3/1
2x < 15
x < 7.5

so x < 7.5 AND x > 10
no such number exists.

your answer of x = 2.4
test:
if x=2.4
4.8/5 = .96 which < 3 BUT NOT > 2