First, divide each side of the equation by color(red)(8) to isolate the absolute value function while keeping the equation balanced:
(8abs(12x + 7))/color(red)(8) = 80/color(red)(8)
(color(red)(cancel(color(black)(8)))abs(12x + 7))/cancel(color(red)(8)) = 10
abs(12x + 7) = 10
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:
12x + 7 = -10
12x + 7 - color(red)(7) = -10 - color(red)(7)
12x + 0 = -17
12x = -17
(12x)/color(red)(12) = -17/color(red)(12)
(color(red)(cancel(color(black)(12)))x)/cancel(color(red)(12)) = -17/12
x = -17/12
Solution 2:
12x + 7 = 10
12x + 7 - color(red)(7) = 10 - color(red)(7)
12x + 0 = 3
12x = 3
(12x)/color(red)(12) = 3/color(red)(12)
(color(red)(cancel(color(black)(12)))x)/cancel(color(red)(12)) = 1/4
x = 1/4
The Solutions Are: x = -17/12 and x = 1/4
