Verified answer

| 6x - 2 | >= 7/3

6x - 2 >= 7/3 or 6x - 2 <= -7/3

6x >= 13/3 or 6x <= -1/3

x >= 13/18 or x <= -1/18

{x: x <= -1/18 or x >= 13/18 }

(If you make x = 0 from your interval, you'll see that the inequality will not be true.)