Question

How do you solve `abs(3x+4)=20`?

Answer 1

See a solution process below:

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:

`3x + 4 = -20`

`3x + 4 - color(red)(4) = -20 - color(red)(4)`

`3x + 0 = -24`

`3x = -24`

`(3x)/color(red)(3) = -24/color(red)(3)`

`(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) = -8`

`x = -8`

Solution 2:

`3x + 4 = 20`

`3x + 4 - color(red)(4) = 20 - color(red)(4)`

`3x + 0 = 16`

`3x = 16`

`(3x)/color(red)(3) = 16/color(red)(3)`

`(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) = 16/3`

`x = 16/3`

The Solution Set Is: `x = {-8, 16/3}`