[tex]|4x-3| \leq -\frac{27}{4} [/tex]

|4x-3|<= -27/4
4x-3<= -27/4
4x<= -27/4+3
4x <= -27/4 + 3/1
4x <= -27/4 + 12/4
4x <= -15/4
x <= -15/4 : 4
x <= -15/16

4x-3 >= 27/4
4x >= 27/4 + 3
4x >= 27/4 + 3/1
4x >= 27/4 + 12/4
4x >= 39/4
HP = { x| -15/16 >= x >= 39/4 }