Question

How do you solve |5x-4|>6

Answer 1

x < -
`(2)/(5)` or x > 2

Explanation:

inequalities of the form | x | > a always have solutions of the form

x < - a or x > a, hence

5x - 4 < - 6 or 5x - 4 > 6 ( add 4 to both sides in both inequalities )

5x < - 2 or 5x > 10 ( divide both sides by 5 in both inequalities )

x < -
`(2)/(5)` or x > 2

The solutions can be expressed in interval notation as

x ∈ (- ∞, -
`(2)/(5)`) ∪ (2, ∞ )