Question

How do you solve `abs(4x-7)=13`?

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:

`4x - 7 = -13`

`4x - 7 + color(red)(7) = -13 + color(red)(7)`

`4x - 0 = -6`

`4x = -6`

`(4x)/color(red)(4) = -6/color(red)(4)`

`(color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4)) = -6/4`

`x = -3/2`

Solution 2:

`4x - 7 = 13`

`4x - 7 + color(red)(7) = 13 + color(red)(7)`

`4x - 0 = 20`

`4x = 20`

`(4x)/color(red)(4) = 20/color(red)(4)`

`(color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4)) = 5`

`x = 5`

The Solutions Are: `x = -3/2` and `x = 5`