Question

How do you solve the equation `abs(3(x-2))=10`?

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:

`color(red)(3)(x - 2) = -10`

`(color(red)(3) xx x) - (color(red)(3) xx 2) = -10`

`3x - 6 = -10`

`3x - 6 + color(red)(6) = -10 + color(red)(6)`

`3x - 0 = -4`

`3x = -4`

`(3x)/color(red)(3) = -4/color(red)(3)`

`(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) = -4/3`

`x = -4/3`

Solution 1:

`color(red)(3)(x - 2) = 10`

`(color(red)(3) xx x) - (color(red)(3) xx 2) = 10`

`3x - 6 = 10`

`3x - 6 + color(red)(6) = 10 + color(red)(6)`

`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 Is: `x = {-4/3, 16/3}`