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.
#-4 < 3k - 2 < 4#
First, add #color(red)(2)# to each segment of the of the system of inequalities to isolate the #k# term while keeping the system balanced:
#-4 + color(red)(2) < 3k - 2 + color(red)(2) < 4 + color(red)(2)#
#-2 < 3k - 0 < 6#
#-2 < 3k < 6#
Next, divide each segment by #color(red)(3)# to solve for #k# while keeping the system balanced:
#-2/color(red)(3) < (3k)/color(red)(3) < 6/color(red)(3)#
#-2/3 < (color(red)(cancel(color(black)(3)))k)/cancel(color(red)(3)) < 2#
#-2/3 < k < 2#
Or
#k > -2/3# and #k < 2#
Or, in interval notation:
#(-2/3, 2)#
