The given inequality is
[tex] | 7x-1| \geq 4 [/tex]
First we need to remove the inequality, and on doing so we will get two inequalities, which are
[tex] 7x-1 \geq 4 \ or \ 7x-1 \leq -4 [/tex]
Adding 1 to both equations
[tex] 7x \geq 5 \ or \ 7x \leq -3 [/tex]
Dividing both sides by 7
[tex] x \geq 5/7 \ or \ x \leq -3/7 [/tex]
So the required solution is
[tex] (- \infty ,-3/7] U ( 5/7, \infty) [/tex]
