Given:

|3x – 7|> 4, x ϵ R.

3x – 7 < -4 or 3x – 7 > 4

(Because |x| > a, a>0 then x < -a and x > a)

3x – 7 < -4

Now, adding 7 to both the sides in the above equation

3x – 7 + 7 < -4 +7

3x < 3

Now, dividing by 3 on both the sides of above equation

x < 1

Now,

3x – 7 > 4

Adding 7 on both the sides in above equation

3x – 7 + 7 > 4 + 7

3x > 11

Now, dividing by 3 on both the sides in the above equation

Therefore,