Question

How do you solve `|5x + 11| = 6`?

Answer 1

See a solution process below: `x = -17/5` and `x = -1`

Explanation:

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

Solution 1:

`5x + 11 = -6`

`5x + 11 - color(red)(11) = -6 - color(red)(11)`

`5x + 0 = -17`

`5x = -17`

`(5x)/color(red)(5) = -17/color(red)(5)`

`(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = -17/5`

`x = -17/5`

Solution 2:

`5x + 11 = 6`

`5x + 11 - color(red)(11) = 6 - color(red)(11)`

`5x + 0 = -5`

`5x = -5`

`(5x)/color(red)(5) = -5/color(red)(5)`

`(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = -1`

`x = -1`

The Solutions Are: `x = -17/5` and `x = -1`