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

The problem contains a double inequality system:
2x+2(4+3x)<2+3x

2+3x>2x+
2
x
​


Let's solve the first inequality:

2x+8+6x<2+3x
8x+8<2+3x
8x−3x<2−8
5x<−6
x<−
5
6
​
⟹x<−1.2
Now, let's solve the second inequality:

2+3x>2x+
2
x
​

2+3x>
2
5x
​

Multiply by 2:

4+6x>5x
6x−5x>−4
x>−4
Combining both results, the range of x is:

−4Let's test the given options against this range:

A) x=−3: Fits within (−4,−1.2)

B) x=1: Does not fit

C) x=0: Does not fit

D) x=−1: Does not fit

Hence, x=−3 is a valid value.