Question

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

|7x - 1| is greater than or equal to 4

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)`