If 2(3x+5)>4x−5<3x+2; then x can take which of the following values?

The given expression consists of a system of two inequalities:
2(3x+5)>4x−5

4x−5<3x+2

Let's solve the first inequality:

2(3x+5)>4x−5
6x+10>4x−5
6x−4x>−5−10
2x>−15
x>−7.5
Let's solve the second inequality:

4x−5<3x+2
4x−3x<2+5
x<7
Combining both inequalities, we get the range for x:

−7.5Now let's check the given options to see which value falls inside this range:

A) 8 (Not in range)

B) 6 (In range, since −7.5<6<7)

C) −8 (Not in range)

D) −10 (Not in range)

Therefore, x can take the value 6.