Question

How do you solve `|8- 3x | = 8`?

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:

`8 - 3x = -`

`8 - color(red)(8) - 3x = -8 - color(red)(8)`

`0 - 3x = -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`

Solution 2:

`8 - 3x = 8`

`8 - color(red)(8) - 3x = 8 - color(red)(8)`

`0 - 3x = 0`

`-3x = 0`

`(-3x)/color(red)(-3) = 0/color(red)(-3)`

`(color(red)(cancel(color(black)(-3)))x)/cancel(color(red)(-3)) = 0`

`x = 0`

The Solution Set Is:

`x = (0, 16/3)`