Answer:
2, 3 , 5, 7
Step-by-step explanation:
2(x - 2)/3 < (x + 1)/2 < 3(5x + 6)/4
Considering:
2(x - 2)/3 < (x + 1)/2
<=>(2x - 4)/3 < (x + 1)/2
<=> (2x - 4)*2 < (x + 1)*3
<=> 4x - 8 < 3x + 3
<=> 4x - 3x < 8 + 3
<=> x < 11
Considering:
(x + 1)/2 < 3(5x + 6)/4
<=>(x + 1)/2 < (15x + 18)/4
<=>(x + 1)*4 < (15x + 18)*2
<=> 4x + 4 < 30x + 36
<=> 4x - 30x < 36 - 4
<=> -26x < 32
<=> 26x > -32
<=> x > -32/26
=> -32/26 < x < 11
The prime numbers satisfy the above inequalities: 2, 3 , 5, 7
