Question

Solve the inequality algebraically. Write the solution in interval notation.

Answer 1

The given inequality is

$| 7x-1| \geq 4$

First we need to remove the inequality, and on doing so we will get two inequalities, which are

$7x-1 \geq 4 \ or \ 7x-1 \leq -4$

Adding 1 to both equations

$7x \geq 5 \ or \ 7x \leq -3$

Dividing both sides by 7

$x \geq 5/7 \ or \ x \leq -3/7$

So the required solution is

$(- \infty ,-3/7] U ( 5/7, \infty)$