Question

How do you solve `abs(1/2x+4)=6`?

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:

`1/2x + 4 = -6`

`1/2x + 4 - color(red)(4) = -6 - color(red)(4)`

`1/2x + 0 = -10`

`1/2x = -10`

`color(red)(2) xx 1/2x = color(red)(2) xx -10`

`color(red)(2)/2x = -20`

`1x = -20`

`x = -20`

Solution 2:

`1/2x + 4 = 6`

`1/2x + 4 - color(red)(4) = 6 - color(red)(4)`

`1/2x + 0 = 2`

`1/2x = 2`

`color(red)(2) xx 1/2x = color(red)(2) xx 2`

`color(red)(2)/2x = 4`

`1x = 4`

`x = 4`

The Solution Set Is: `x = {-20, 4}`