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}
