First, add #color(red)(9)# to each side of the equation to isolate the absolute value term while keeping the equation balanced:
#7abs(10v - 2) - 9 + color(red)(9) = 5 + color(red)(9)#
#7abs(10v - 2) - 0 = 14#
#7abs(10v - 2) = 14#
Next, divide each side of the equation by #color(red)(7)# to isolate the absolute value function while keeping the equation balanced:
#(7abs(10v - 2))/color(red)(7) = 14/color(red)(7)#
#(color(red)(cancel(color(black)(7)))abs(10v - 2))/cancel(color(red)(7)) = 2#
#abs(10v - 2) = 2#
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:
#10v - 2 = -2#
#10v - 2 + color(red)(2) = -2 + color(red)(2)#
#10v - 0 = 0#
#10v = 0#
#(10v)/color(red)(10) = 0/color(red)(10)#
#(color(red)(cancel(color(black)(10)))v)/cancel(color(red)(10)) = 0#
#v = 0#
Solution 2:
#10v - 2 = 2#
#10v - 2 + color(red)(2) = 2 + color(red)(2)#
#10v - 0 = 4#
#10v = 4#
#(10v)/color(red)(10) = 4/color(red)(10)#
#(color(red)(cancel(color(black)(10)))v)/cancel(color(red)(10)) = 2/5#
#v = 2/5#
The Solution Set Is: #v = {0, 2/5}#
