First, add #color(red)(41)# to each side of the equation to isolate the absolute value term while keeping the equation balanced:
#2abs(v + 4) - 41+ color(red)(41) = -15 + color(red)(41)#
#2abs(v + 4) - 0 = 26#
#2abs(v + 4) = 26#
Next, divide each side of the equation by #color(red)(2)# to isolate the absolute value function while keeping the equation balanced:
#(2abs(v + 4))/color(red)(2) = 26/color(red)(2)#
#(color(red)(cancel(color(black)(2)))abs(v + 4))/cancel(color(red)(2)) = 13#
#abs(v + 4) = 13#
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:
#v + 4 = -13#
#v + 4 - color(red)(4) = -13 - color(red)(4)#
#v + 0 = -17#
#v = -17#
Solution 1:
#v + 4 = 13#
#v + 4 - color(red)(4) = 13 - color(red)(4)#
#v + 0 = 9#
#v = 9#
The Solution Is:
#v = {-17, 9}#
