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#
