Question

How do you solve and write the following in interval notation: `| 3x | + 5 > 14`?

Answer 1

See the entire solution process below:

Explanation:

First, subtract `color(red)(5)` from each side of the equation to isolate the absolute value function:

`abs(3x) + 5 - color(red)(5) > 14 - color(red)(5)`

`abs(3x) + 0 > 9`

`abs(3x) > 9`

The absolute value function takes any negative or positive term and transforms it to its positive form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

`-9 > 3x > 9`

`-9/color(red)(3) > (3x)/color(red)(3) > 9/color(red)(3)`

`-3 > (color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) > 3`

`-3 > x > 3`

Or

`x < -3` and `x > 3`

Or

`(oo, -3)` and `(3, oo)`